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This research work is dedicated to an investigation for a new kind of boundary value problem of nonlinear fractional differential equation supplemented with general boundary condition. A full analysis of existence and uniqueness of positive solutions is respectively proved by Leray–Schauder nonlinear alternative theorem and Boyd–Wong’s contraction principles. Furthermore, we prove the Hyers–Ulam (HU) stability and Hyers–Ulam–Rassias (HUR) stability of solutions. An example illustrating the validity of the existence result is also discussed.

In this article, by using the Schauder fixed point theorem, we first study the existence of solutions for a new coupled system of Caputo fractional differential equations with multipoint boundary value conditions under the assumption that the nonlinear term satisfies two types of the Carathéodory conditions. Using this result, we provide the existence of solutions of the system with infinite points and Riemann–Stieltjes integral boundary conditions, respectively, instead of doing it directly. Finally, we give three examples to illustrate the feasibility of main results.

Based on properties of Green’s function and by Avery–Peterson fixed point theorem, the existence of multiple positive solutions are obtained for singular p-Laplacian fractional differential equation with infinite-point boundary conditions, and an example is given to demonstrate the validity of our main results.

This paper investigates the abstract fractional stochastic evolution equations. A new existence result of the square-mean S-asymptotically periodic mild solutions are obtained under the assumption that the nonlinear terms only satisfy some growth conditions. Moreover, the uniqueness and asymptotic stability results of the square-mean S-asymptotically periodic solution are presented when the nonlinear functions satisfy the general Lipschitz condition. Finally, two examples are given to illustrate our main results. MR(2020) Subject Classification: 60H15; 47D06; 34G20; 46T20.

In this paper, as an extension of the isotone projection cone, we consider the isotonicity of the metric projection operator with respect to the mutually dual orders induced by the cone and its dua...

In this paper, we consider the Cauchy problem for the 2D inviscid Boussinesq equations with N being the buoyancy frequency. It is proved that for general initial data u 0 ∈ H s with s > 3 , the life span of the classical solutions satisfies T > C ln N 3 / 4 .

In this paper, we study the mild solutions of a class of nonlinear fractional reaction–diffusion equations with delay and Caputo’s fractional derivatives. By the measure of noncompactness, the theory of resolvent operators, the fixed point theorem and the Banach contraction mapping principle, we develop various theorems for the existence and uniqueness of the global mild solutions for the problem.

In this article, we first discuss the subduality and orthogonality of the cones and the dual cones when the norm is monotone in Banach spaces. Then, under different assumptions, the necessary and s...

We investigate a class of semipositone fractional integral boundary value problem on the half-line. Using the fixed point index theorems in a cone, we obtain the existence result of positive solutions.

An input vector composed of various features plays an important role in short-term traffic forecasting. However, there is limited research on the optimal feature selection of an input vector for a certain forecasting task. To fill the gap, this paper proposes a cohesion-based heuristic feature selection method by analyzing the nature of the forecasting methods. This method is able to determine which features should be contained in an input vector to make a forecasting algorithm perform better. The proposed method is demonstrated in two experiments based on the empirical traffic flow data. The results show that the method is able to improve the performances of the short-term traffic forecasting algorithms. It is then suggested to consider the proposed method as a preprocessing procedure in practical forecasting applications.

This paper discusses the abstract time-space fractional evolution equation with the Caputo derivative of order $$\alpha \in (0,1)$$ and fractional power operator $$-A^{\beta }$$ , $$\beta \in (0,1)$$ , where $$-A$$ generates a $$C_{0}$$ -semigroup on a Banach space. The compactness and exponential stability of the semigroup which is generated by fractional power operator $$-A^{\beta }$$ are investigated. With the aid of the properties of the semigroup, the existence and global asymptotic behavior of S-asymptotically periodic solutions are obtained by some fixed point theorems and related inequalities. An example to the time-space fractional diffusion equation with fractional Laplacian will be shown.

Low-carbon innovation can address both economic and environmental concerns; patterns of low-carbon innovation convergence can determine the effectiveness of mitigating the adverse consequences of climate change. Considering that economic openness has a huge impact on the development of innovation capability, this paper uses a conditional β convergence model to examine the convergence of low-carbon innovation in Chinese manufacturing industry and its relationship with economic openness. We incorporate the spatial spillover effect into the convergence function by constructing spatial error model, spatial lag model, and spatial Durbin model. Based on a panel data set of 30 Chinese provinces over the period 2004–2016, the results show that low-carbon innovation in Chinese manufacturing industry has a strong feature of conditional β convergence. The convergence rate of low-carbon innovation is slightly slowed down by economic openness, and the main reason is that the spillover effect is weak and the convergence rate is slow in lower open areas, so the convergence rate of the whole country is slowed down by that of the lower open areas. Although the economic openness in adjacent areas can contribute to the development of local innovation ability, but generally speaking, economic openness in local areas takes a stronger effect in promoting the convergence of low-carbon innovation than that in adjacent areas. The findings have important policy implications as they suggest the need for a more equal degree of economic openness among Chinese provinces to speed up the convergence of low-carbon innovation.

A Kirchhoff-type problem with concave-convex nonlinearities is studied. By constrained variational methods on a Nehari manifold, we prove that this problem has a sign-changing solution with least energy. Moreover, we show that the energy level of this sign-changing solution is strictly larger than the double energy level of the ground state solution.

In this paper, we present a new fixed point theorem for the sum of two mixed monotone operators of Meir–Keeler type on ordered Banach spaces through projective metric, which extends the existing corresponding results. As applications, we utilize the results obtained in this paper to study the existence and uniqueness of positive solutions for nonlinear singular fourth-order elastic beam equations with nonlinear boundary conditions.

In this paper, we study the initial boundary value problem for a Petrovsky type equation with a memory term, a linear weak damping and superlinear source. Finite time blow-up results have been obtained for the case in which the initial energy $$E(0)\le M$$ , where M is a positive constant. By utilizing Levine’s classical concavity method, we give a new blow-up criterion which includes the case of $$E(0)>M$$ and derive an explicit upper bound for the blow-up time. By using the Fountain Theorem, we show that the problem with arbitrary positive initial energy always admits weak solutions blowing up in finite time.

In this paper, the isotonicity of the proximity operator and its applications are discussed. We first establish a few new conditions of the mappings such that their proximity operators are isotone with respect to orders induced different minihedral cones. Some properties and examples for these conditions are then introduced. We especially consider the isotonicity of the proximity operator with respect to one order induced by a subdual cone and two orders. To estimate the convergence rate of the iterative algorithms, some other inequality characterizations of the proximity operator with respect to the orders are then proved. As applications, some solvability and approximation theorems for the mixed variational inequality and optimization problems are established by order approaches, in which the mappings need not to be continuous and the solutions are optimal with respect to the orders. By using the isotonicity of the proximity operator with respect to two orders, we overcome the absence of the regularity of the order. The convergence rate of forward–backward algorithms is finally estimated by order approaches.

This paper focuses on a class of hider-order nonlinear fractional boundary value problems. The boundary conditions contain Riemann–Stieltjes integral and nonlocal multipoint boundary conditions. It is worth mentioning that the nonlinear term and the boundary conditions contain fractional derivatives of different orders. Based on the Schauder fixed point theorem, we obtain the existence of solutions under the hypothesis that the nonlinear term satisfies the Carathéodory conditions. We apply the Banach contraction mapping principle to obtain the uniqueness of solutions. Moreover, by using the theory of spectral radius we prove the uniqueness and nonexistence of positive solutions. Finally, we illustrate our main results by some examples.

In this paper, by using the cosine family theory, measure of non-compactness and the generalization of Darbo-fixed point theorem, we establish the existence of mild solutions of nonlinear second-order impulsive integro-differential evolution equations of Volterra type in Banach spaces. The result obtained herein generalizes and improves some known results.

In this paper, we establish the results of nonexistence and existence of blow-up radial solutions for a k-Hessian equation with a nonlinear operator. Under some suitable growth conditions for nonlinearity, the result of nonexistence of blow-up solutions is established, a sufficient and necessary condition on existence of blow-up solutions is given, and some further results are obtained.

In the paper, we prove that the N -Kirchhoff type problem in R N has at least three solutions by using the Ekeland variational principle and fibering map.

Electrochemical reduction reaction of nitric oxide (NORR) to ammonia has been considered as a promising alternative to capturing and utilizing NO emitted from thermal-power plants. Various metal-containing catalysts have been proved to possess efficient catalytic activities for NORR, yet the attempt on metal-free NORR catalysts is quite limited. Herein, by employing first-principle calculations, we propose a novel strategy of designing metal-free NORR catalyst by introducing Ccenter-CN2 configuration into hexagonal boron nitride-graphene heterostructures (hBN-graphene). The hBN-graphene heterostructures demonstrate excellent NORR activity, achieving a fairly low limiting potential of −0.22 V. The superior NORR activity is ascribed to the introduced unique configuration at the modified hBN-graphene interface. Moreover, the hBN-graphene heterostructures can efficiently suppress hydrogen evolution—the main competitive reaction. The ab-initio molecular dynamic simulations indicate that hBN-graphene heterostructures can retain considerable thermal stability. Our work opens an avenue to design metal-free catalysts for NORR by modulating the interface in two-dimensional heterostructures.

Energy is a key factor regulated by the neuroendocrine system. The objective of this study was to compare growth performance, serum biochemical indices, carcass traits, meat quality, and nutrient composition of lambs fed restricted metabolizable energy (ME) intakes to mimic the seasonal changes of the natural grasslands of northwest China. Nineteen male Dorper × Small Tailed Han lambs were assigned to treatments, control (CON) fed at 1.0 MJ/W(0.75) × d(−1) throughout the 180 d study, and restricted ME (RES) fed by sequentially restricting ME every 30 d (0.56, 0.84, 1.0, 0.84, 0.56, and 0.28 MJ/W(0.75) × d(−1)). Lambs were harvested at the end of the study. Lambs fed the CON diet demonstrated higher (P < 0.05) average daily gain (ADG) compared with RES-fed lambs (158.79 and 57.01 g/d, for CON and RES, respectively), although ADG were lower in each period with the last period being a negative ADG for RES-fed lambs resulting in a loss of body weight. Both treatments demonstrated lower ADG in the last 3 study periods compared with the first 2 periods, which may be explained by cold stress ( 0.05) for cholesterol and high-density lipoprotein-cholesterol. Feeding lambs a restricted ME diet increased (P < 0.05) meat pH, while reducing the cooked meat rate compared with CON-fed lambs. Thus, the carcass yield, rib eye muscle area, and shear force were lower (P < 0.05) for RES-fed lambs compared with CON-fed lambs. The meat water concentration was higher (P < 0.05), whereas the concentrations of dry matter, crude fat, crude protein, and carbohydrate were lower (P < 0.05) for lambs fed a RES ME diet compared to CON-fed lambs. These results demonstrate that sequentially restricting ME intake, as natural grasslands might experience during seasonal forage quality and quantity changes, resulted in a reduction of body weight because lambs were mobilizing body reserves as a source of ME. The reduction in concentrations of key serum nutrients, as well as carcass traits and meat composition, demonstrate the body is responding to the meet the lambs ME requirements, which has implications for both meat quality and the animal’s physiological functions.

In this paper, we establish the existence and nonexistence of radial solutions of the Dirichlet problem for a class of general k-Hessian equations in a ball. Under some suitable local growth conditions for nonlinearity, several new results are obtained by using the fixed-point theorem.

We study the existence and uniqueness of positive solution for a class of nonlinear binary operator equations systems by means of the cone theory and monotone iterative technique, under more general conditions. Also, we give the iterative sequence of the solution and the error estimation of the system. Moreover, we use this new result to study the existence and uniqueness of the solutions for fractional differential equations systems involving integral boundary value conditions in ordered Banach spaces as an application. The results obtained in this paper are more general than many previous results and complement them.

In this paper, we establish some new results on the existence and nonexistence of radial large positive solutions for a modified Schrodinger system with a nonconvex diffusion term by a successive iteration technique and the dual approach. The necessary and sufficient condition for the existence of radial large positive solutions is established. Our results improve and extend many previous work in this field of research.

In this paper we investigate a system of impulsive integral boundary value problems with sign-changing nonlinearities. Using the fixed point theorem in double cones, we prove the existence of multiple positive solutions.

In the paper, we study two classes of optimal reinsurance problems on Orlicz hearts in which both the insurer and reinsurer face risk and uncertainty. Based on Balbas et al. (2015) and Rockafellar and Royset (2015b), we first establish the robust representations for the mixed C V a R relative to the set of priors P U 0 . Then we introduce the general reinsurance premium principle and the general optimal reinsurance problems, which include most of the existing problems as special cases. The necessary and sufficient optimality conditions of the optimal reinsurance problems are obtained by different dual approaches under more general assumptions.

In this paper, we study the initial boundary value problem for a class of parabolic or pseudo-parabolic equations: u t − a Δ u t − Δ u + b u = k ( t ) | u | p − 2 u , ( x , t ) ∈ Ω × ( 0 , T ) , where a ≥ 0 , b > − l 1 with l 1 being the principal eigenvalue for − Δ on H 0 1 ( Ω ) and k ( t ) > 0 . By using the potential well method, Levine’s concavity method and some differential inequality techniques, we obtain the finite time blow-up results provided that the initial energy satisfies three conditions: (i) J ( u 0 ; 0 ) 0 ; (ii) J ( u 0 ; 0 ) ≤ d ( ∞ ) , where d ( ∞ ) is a nonnegative constant; (iii) 0 J ( u 0 ; 0 ) ≤ C ρ ( 0 ) , where ρ ( 0 ) involves the L 2 -norm or H 0 1 -norm of the initial data. We also establish the lower and upper bounds for the blow-up time. In particular, we obtain the existence of certain solutions blowing up in finite time with initial data at the Nehari manifold or at arbitrary energy level.

In this paper, we study a three-dimensional (3D) viscoelastic wave equation with nonlinear weak damping, supercritical sources and prescribed past history u0(x,t) , t≤0 : utt-k(0)Δu-∫0+∞k′(s)Δu(t-s...

In this paper, we investigate the existence of nontrivial solutions for a class of fractional advection–dispersion systems. The approach is based on the variational method by introducing a suitable fractional derivative Sobolev space. We take two examples to demonstrate the main results.

An electron spin echo envelope modulation (ESEEM) approach was used to probe local secondary structures of membrane proteins and peptides. This ESEEM method detects dipolar couplings between 2H-labeled nuclei on the side chains of an amino acid (Leu or Val) and a strategically placed nitroxide spin-label in the proximity up to 8 A. ESEEM spectra patterns for different samples correlate directly to the periodic structural feature of different secondary structures. Since this pattern can be affected by the side chain length and flexibility of the 2H-labeled amino acid used in the experiment, it is important to examine several different hydrophobic amino acids (d3 Ala, d8 Val, d8 Phe) utilizing this ESEEM approach. In this work, a series of ESEEM data were collected on the AChR M2δ membrane peptide to build a reference for the future application of this approach for various biological systems. The results indicate that, despite the relative intensity and signal-to-noise level, all amino acids share a similar...

In this paper, we investigate the existence of nontrivial weak solution for a Schrodinger–Kirchhoff-type system driven by a $$(p_1,p_2)$$ -Laplacian operator under appropriate hypotheses. The proofs are based on the variational methods.

In this paper, we consider the initial boundary value problem for a class of thin-film equations in R n with a p-Laplace term and a nonlocal source term | u | q − 2 u − 1 | Ω | ∫ Ω | u | q − 2 u dx . We prove that there exist weak solutions for the problem with arbitrarily initial energy that blow up in finite time. We also obtain the upper bounds for the blow-up time.

In this paper, we study a class of nonlinear singular system with coupled integral boundary condition. Based on the Guo–Krasnosel'skii fixed point theorem, some new results on the existence of symmetric positive solutions for the coupled singular system are obtained. The impact of the two different parameters on the existence of symmetric positive solutions is also investigated. Finally, an example is then given to demonstrate the applicability of our results.

In this paper, we consider the uniqueness of nontrivial positive radial solutions to the following Schrodinger system with linear and nonlinear couplings: { − △ u 1 + V 1 ( x ) u 1 = μ 1 u 1 3 + β u 1 u 2 2 + κ u 2 in R N , − △ u 2 + V 2 ( x ) u 2 = μ 2 u 2 3 + β u 1 2 u 2 + κ u 1 in R N , u 1 ( x ) , u 2 ( x ) > 0 in R N ( N ≤ 3 ) , u 1 ( x ) , u 2 ( x ) → 0 as | x | → ∞ . By using the a priori estimate technique, we obtain interesting uniqueness results for two cases: (1) sufficiently small β , κ > 0 , (2) large β > 0 .

Ammonia (NH3) has been regarded as an attractive energy source for hydrogen production via catalytic decomposition, especially over non-noble metal catalysts. Owing to the decent performance and low cost, nickel (Ni) based catalysts have been widely studied for catalytic decomposition of NH3 where the decomposition rates, can be further tailored by adding other metals. Herein, we synthesized bimetallic M(M = Co, Fe, Cu)Ni/Al2O3 catalysts delivering superior catalytic performance at a wide temperature range of 350–750 °C. Co-Ni/Al2O3 demonstrated nearly 100% conversion of NH3 decomposition to H2 at 700 °C and the gas hourly space velocity of 30,000 ml g−1 min−1, which was ~20.85% higher than that of intrinsic Ni/Al2O3. The structural characterizations indicated that Co could decrease the particle size and enhance the dispersion of active sites. The density functional theory calculations substantiated that the associative decomposition of N to generate N2 was the rate-determining step of the NH3 decomposition reactions. NH3 Temperature Programmed Desorption (TPD) results suggested that the enhanced catalytic performance was predominantly attributed to the Co that decreases the energy barrier for the associative decomposition of N to form N2. This study provides new insights in designing diverse catalysts for efficient NH3 decomposition for controllable H2 production.

In this paper, we study the entire blow-up solutions for a quasilinear p -Laplacian Schrodinger elliptic equation with a non-square diffusion term. By using the dual approach and some new iterative techniques, the difficulty due to the non-square diffusion term and the p -Laplacian operator is overcome and the nonexistence and existence of entire blow-up solutions are established.

In this paper, we investigate the initial boundary value problem for a pseudo-parabolic equation under the influence of a linear memory term and a nonlinear source term ut-Δu-Δut+∫0tg(t-τ)Δu(τ)dτ=|...

By introducing a subspace of H 2 ( Ω ) with constraints ∂ u ∂ n | ∂ Ω = 0 and ∫ Ω u d x = 0 and using the Fountain Theorem, we obtain the existence of infinitely many sign-changing high energy solutions for a biharmonic equations with p -Laplacian and Neumann boundary condition.

In order to investigate the largest motor vehicle ownership load within the scope of a city with atmospheric environmental indicators as constraint, this article estimates traffic atmospheric environmental capacity (TAEC) and carrying capacity (TAECC) in Tianjin using the A-value method recommended by the Chinese national standard. Our results indicate that NO X carrying capacity is a key restraining factor of TAEC. According to the current vehicle emission levels per year and air quality standard, Tianjin can accommodate 4.21 million vehicles. Classified by the vehicle type, heavy trucks and large-sized passenger cars are identified as the most important restrictive factors of TAECC. Then we analyze change of TAECC and TAECC’s service life under the circumstances of clean vehicle strategy and mobility management strategy. Clean vehicles strategy represented by the elimination of heavy-polluting vehicles can reduce emissions of vehicles so that it can rapidly enhance the TAECC in the short term. Mobility management strategy represented by the car purchase restriction, which reduces total motor vehicle travel, is indispensable for improvement of TAECC in the long term. On the whole, the clean vehicles strategy and mobility management strategy should be implemented gradually.