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This paper considers a nonlinear model for population dynamics with age structure. The fertility rate with respect to age is non constant and has the form proposed by [17]. Moreover, its multiplicative structure and the multiplicative structure of mortality makes the model separable. In this setting it is shown that the number of births in unit time is given by a system of nonlinear ordinary differential equations. The steady state solution together with the equilibrium solution is found explicitly.

This paper considers a stochastic production planning problem with regime switching. There are two regimes corresponding to different economic cycles. A factory is planning its production so as to minimize production costs. We analyze this problem through the value function approach. The optimal production is characterized through the solution of an elliptic system of partial differential equations which is shown to have a solution.

Stochastic production planning problems were studied in several works; the model with one production good was discussed in [3]. The extension to several economic goods is not a trivial issue as one can see from the recent works [4], [5] and [6]. The following qualitative aspects of the problem are analyzed in [5]; the existence of a solution and its characterization through dynamic programming/HJB equation, as well as the verification (i.e., the solution of the HJB equation yields the optimal production of the goods). In this paper, we stylize the model of [4] and [5] in order to provide some quantitative answers to the problem. This is possible especially because we manage to solve the HJB equation in closed form. Among other results, we find that the optimal production rates are the same across all the goods and they also turn to be independent of some model parameters. Moreover we show that production rates are increasing in the aggregate number of goods produced, and they are also uniformly bounded. Numerical experiments show some patterns of the output.

This paper deals with the existence of solutions for an elliptic system of partial differential equations. The solution method is based on the sub- and super-solutions approach. An application to a stochastic control problem is presented. This system seemed not considered before., Comment: arXiv admin note: text overlap with arXiv:1907.04520

This paper deals with the following elliptic equation \begin{equation*} -2\sigma^{2}\Delta z+\left\| \nabla z\right\| ^{2}+4\alpha z=4\left\| x\right\| ^{2}\text{ for }x\in \mathbb{R}^{N}\text{, (}% N\geq 1\text{),} \end{equation*}% where $\alpha >0,$ $\sigma>0$ are some real parameters. The solution method is based on the sub- and super-solutions approach. The case $N>1$ seemed not considered before. This equation models a stochastic production planning problem.

In this article we consider the question of the existence of positive symmetric solutions to the problems of the following type $\Delta u=a\left( \left\vert x\right\vert \right) h\left( u\right) +b\left( \left\vert x\right\vert \right) g\left( u\right) $ for $x\in \mathbb{R}^{N}$, which are called entire large solutions. Here $N\geq 3$, and we assume that $a$ and $b$ are nonnegative continuous spherically symmetric functions on $\mathbb{R}% ^{N} $. We extend results previously obtained for special cases of $h$ and $% g $ and we will describe a real-world model in which such problems may arise.

In this paper, we establish conditions on the weights that are necessary and sufficient for the existence of positive solutions, bounded and unbounded, of a semilinear elliptic system., Comment: arXiv admin note: text overlap with arXiv:1603.04356

In this paper, we are concerned with the existence of nonnegative solutions for a nonlinear elliptic system. Our results are obtained by an application of the Arzela--Ascoli theorem.

In this paper, two new results and short proofs are given for the existence of positive entire large and bounded radial positive solutions for a nonlinear system with gradient term. Our results complete and improve a recently work published by Zhang and Zhou. The main difficulty in dealing with our system is the presence of the convection term.

In the present paper, we are concerned with entire radially symmetric solutions for a quasilinear system with phi{i}-Laplacian operator., Comment: arXiv admin note: text overlap with arXiv:1509.01494

This work proposes to generalize certain results regarding some semilinear elliptic systems.

In this paper, we study the existence of positive entire large and bounded radial positive solutions for a nonlinear system. Our results give an answer of the question raised in [11].

In this article we consider the existence of positive radial solutions for Hessian equations and systems with weights and we give a necessary condition as well as a sufficient condition for a positive radial solution to be large. The method of proving theorems is essentially based on a successive approximation. Our results complete and improve a recently work published by Zhang and Zhou (Existence of entire positive k-convex radial solutions to Hessian equations and systems with weights, Applied Mathematics Letters, Volume 50, December 2015, Pages 48--55).

A delicate problem is to obtain existence of solutions to the boundary blow-up elliptic equation% \begin{equation*} \sigma _{k}^{1/k}\left( \lambda \left( D^{2}u\right) \right) =g\left( u\right) \text{ in }\Omega \text{, }\underset{x\rightarrow x_{0}}{\lim }% u\left( x\right) =+\infty \text{ }\forall x_{0}\in \partial \Omega \text{,} \end{equation*}% where $\sigma _{k}^{1/k}\left( \lambda \left( D^{2}u\right) \right) $ is the $k$-Hessian operator and $\Omega \subset \mathbb{R}^{N}$ is a smooth bounded domain. Our goal is to provide a necessary and sufficient condition on $g$ to ensure existence of at least one positive blow-up solution. The main tools for proving existence are the comparison principle and the method of sub and supersolutions.

One of the problems faced by a firm that sells certain commodities is to determine the number of products that it must supply in order to maximize its profit. In this article, the authors give an answer to this problem of economic interest. The proposed problem is a generalization of the results obtained by Stirzaker (Probability and Random Variables: A Beginner's Guide, 1999) and Kupferman (Lecture Notes in Probability, 2009) where the authors do not present a situation where the sale of a quantity from some commodities is constrained by the marketing of another. In addition, the described procedure is simple and can be successfully applied to any number of commodities. The obtained results can be easily put into practice.

The present paper concerns with the existence of blow-up solution for a class of elliptic system with convection term. Here, we prove a result involving sub and supersolution for a class of elliptic system whose nonlinearity can depend of the gradient of the solution. This result permits to study the existence of blow-up solution for a large class of systems., Comment: Revised version

We show the existence of solution for some classes of nonlocal problems. Our proof combines the presence of sub and supersolution with the pseudomonotone operators theory.

Boundedness and blow-up of solutions for a nonlinear elliptic system arising in probability and stochastic processes

We deal with existence of entire solutions for the quasilinear elliptic system of this type {\Delta}_{p}u_{i}+h_{i}(|x|)|\bigtriangledown u_{i}|^{p-1}=a_{i}(|x|)f_{i}(u_1,u_2) on R^{N} (N\geq3, i=1,2) where N-1\geqp>1, {\Delta}_{p} is the p-Laplacian operator and h_{i}, a_{i}, f_{i} are suitable functions. The results of this paper supplement the existing results in the literature and improve those obtained by Xinguang Zhang and Lishan Liu, The existence and nonexistence of entire positive solutions of semilinear elliptic systems with gradient term, Journal of Mathematical Analysis and Applications, Volume 371, Issue 1, 1 November 2010, Pages 300-308)., Comment: 10 pages

In this paper we analyze the existence of entire radially symmetric solutions for Schrodinger system type {\Delta}_{p_{i}}u_{i}+h_{i}(r)|\nabla u_{i}|^{p_{i}-1}=a_{i}(r)f_{i}(u_1,...,u_{d}) for i=1,...,d on R^{N} where p_{i}>1, d \in {1,2,3,...}, h_{i} and a_{i} are nonnegative radial continuous functions and f_{i} are nonnegative increasing continuous functions on [0,\infty)., Comment: 10 pages

In this paper we analyze the existence of large positive radial solutions to some quasilinear elliptic systems. Also, a non-radially symmetric solution is obtained by using a lower and upper solution method. The equations are coupled by functions which are increasing with respect to all the variables., Comment: 12 pages

In this article we consider the system of equations {\Delta}u_{i}=p_{i}(x)f_{i}(u_{1},...,u_{d}) for i=1,...,d on R^{N}, N\geq3 and d\in{1,2,3,4,...}. We prove that the considered system has a bounded positive entire solution under some conditions on p_{i} and f_{i}. Also, we give a necessary condition as well as a sufficient condition for a positive radial solution to be large. The method of proving theorems is essentially based on a successive approximation. Furthermore, a non-radially symmetric solution is obtained by using a lower and upper solution method., Comment: to appear in Funkcialaj Ekvacioj

In this paper we obtain existence results for the positive solution of a singular elliptic boundary value problem. To prove the main results we use comparison arguments and the method of sub-super solutions combined with a procedure which truncates the singularity., Comment: to appear in Surveys in Mathematics and its Applications

In this paper we obtain the existence of bounded positive entire radial solutions for the following nonlinear elliptic problem with a special nonlinear gradient term -\triangle_{p}u-b(x)|\nablau|^{p-1}=a(x)f(u), x\inR^{N} (N\geq3), lim_{|x|\rightarrow \infty}u(x)=0, where \triangle_{p}u=div[big]\big(|\nablau|^{p-2}\nablau[big]\big), 1

The purpose of this paper is to prove some existence and non-existence theorems for the nonlinear elliptic problems of the form -{\Delta}_{p}u={\lambda}k(x)u^{q}\pmh(x)u^{{\sigma}} if x\in{\Omega}, subject to the Dirichlet conditions u_{1}=u_{2}=0 on \partial{\Omega}. In the proofs of our results we use the sub-super solutions method and variational arguments. Related results as obtained here have been established in [Z. Guo and Z. Zhang, W^{1,p} versus C^{1} local minimizers and multiplicity results for quasilinear elliptic equations, Journal of Mathematical Analysis and Applications, Volume 286, Issue 1, Pages 32-50, 1 October 2003.] for the case k(x)=h(x)=1. Our results reveal some interesting behavior of the solutions due to the interaction between convex-concave nonlinearities and variable potentials., Comment: 10 pages