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There is substantial literature going back to 1965 showing boundedness properties of solutions of the integro-differential equation ... when A is a positive kernel and h is a continuous function using ... In that study there emerges the pair: Integro-differential equation and Supremum norm. In this paper we study qualitative properties of solutions of integral equations using the same inequality and obtain results on Lp solutions. That is, there occurs the pair: Integral equations and Lp norm. The paper also offers many examples showing how to use the Lp idea effectively. [ABSTRACT FROM AUTHOR]

In this paper, by using Krasnoselskii's fixed point theorem, we study the existence and multiplicity of positive periodic solutions for the delay Nicholson's blowflies model with impulsive effects. Our results show that these positive periodic solutions are generated by impulses. To the authors' knowledge, there are no papers about positive periodic solution generated by impulses for first order delay differential equation. Our results are completely new. Finally, some examples are given to illustrate our main results. [ABSTRACT FROM AUTHOR]

This paper considers two-point higher order impulsive boundary value problems, with a strongly nonlinear fully differential equation with an increasing homeomorphism. It is stressed that the impulsive effects are defined by very general functions, that can depend on the unknown function and its derivatives, till order n - 1. The arguments are based on the lower and upper solutions method, together with Leray-Schauder fixed point theorem. An application, to estimate the bending of a onesided clamped beam under some impulsive forces, is given in the last section. [ABSTRACT FROM AUTHOR]

This paper deals with impulsive problems consisting of second order differential equation with impulsive effects depending implicitly on the solution and with rather general nonlocal boundary conditions. The arguments are based on the lower and upper solutions method and a fixed point theorem. [ABSTRACT FROM AUTHOR]

This paper is concerned with the following fourth-order three-point boundary value problem ... where n ∊ [1/3, 1). In spite of sign-changing Green's function, for arbitrary positive integer n (≥ 2), we still obtain the existence of at least n - 1 decreasing positive solutions to the above problem by imposing some suitable conditions on f . The main tool used is the fixed point index theory. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the second-order problem with dependence on derivative in nonlinearity and Stieltjes integral boundary condition ... where f : [0, 1] × R+ × R+ → R+ is continuous and α[u] is a linear functional. Some inequality conditions on nonlinearity f and the spectral radius conditions of linear operators are presented that guarantee the existence of positive solutions to the problem by the theory of fixed point index on a special cone in C¹[0, 1]. The conditions allow that f (t, x1, x2) has superlinear or sublinear growth in x1, x2. Some examples are given to illustrate the theorems respectively under multi-point and integral boundary conditions with sign-changing coefficients. [ABSTRACT FROM AUTHOR]

In this paper, we study the controllability of a system governed by second order delay differential equations. We introduce a delay Gramian matrix involving the delayed matrix sine, which is used to establish sufficient and necessary conditions of controllability for the linear problem. In addition, we also construct a specific control function for controllability. For the nonlinear problem, we construct a control function and transfer the controllability problem to a fixed point problem for a suitable operator. We give a sufficient condition to guarantee the nonlinear delay system is controllable. Two examples are given to illustrate our theoretical results by calculating a specific control function and inverse of a delay Gramian matrix. [ABSTRACT FROM AUTHOR]

This paper is concerned with the existence of bounded or unbounded solutions to regular and singular second order boundary value problem on the half-line with functional boundary conditions. These functional boundary conditions generalize the usual boundary assumptions and may be applied to a broad number of cases, such as, nonlocal, integro-differential, with delays, with maximum or minimum arguments. . . The arguments are based on the Schauder fixed point theorem and lower and upper solutions method. [ABSTRACT FROM AUTHOR]

In this paper we extend the work begun in 1998 by the author and Kirk for integral equations in which we combined Krasnoselskii's fixed point theorem on the sum of two operators with Schaefer's fixed point theorem. Schaefer's theorem eliminates a difficult hypothesis in Krasnoselskii's theorem, but requires an a priori bound on solutions. Here, we simplify the work by means of a transformation which often reduces the a priori bound to a triviality. Our work is focused on an integral equation in which the goal is to prove that there is a unique continuous positive solution on [0,∞]. In addition to the transformation, there are two techniques which we would emphasize. A technique is introduced yielding a lower bound on the solutions which enables us to deal with problems threatening non-uniqueness. The technique offers a solution to a classical problem and it seems entirely new. We show that when the equation defines the sum of a contraction and a Lipschitz operator, then we first get existence on arbitrary intervals [0, E] and then introduce a technique which we call a progressive contraction which allows us to prove uniqueness and then parlay the solution to [0,∞). The technique is well suited to integral equations. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to investigate the existence and uniqueness of convex monotone positive solutions for a boundary value problem of an elastic beam equation with a parameter. The proofs of the main results rely on a fixed point theorem and some properties of eigenvalue problems for a class of general mixed monotone operators. The results can guarantee the existence of a unique convex monotone positive solution and can be applied to construct two iterative sequences for approximating it. Moreover, we present some pleasant properties of convex monotone positive solutions for the boundary value problem dependent on the parameter. Finally, an example is given to illustrate the main results. [ABSTRACT FROM AUTHOR]

In this paper, we apply Schauder's fixed point theorem, the upper and lower solution method, and topological degree theory to establish the existence of unbounded solutions for the following fourth order three-point boundary value problem on a halfline ... where η ∊ (0,+∞), but fixed, and f : [0,+∞) × R4 → R satisfies Nagumo's condition. We present easily verifiable sufficient conditions for the existence of at least one solution, and at least three solutions of this problem. We also give two examples to illustrate the importance of our results. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a class of stochastic evolution inclusions of Clarke's subdifferential type in Hilbert spaces. The existence of mild solutions and controllability results are given and proved by using stochastic analysis techniques, semigroup of operators theory, a fixed point theorem of multivalued maps and properties of generalized Clarke subdifferential. An example is included to illustrate the applicability of the main results. [ABSTRACT FROM AUTHOR]

In this paper, we study a class of Lasota-Wazewska model with distributed delays, new criteria for the existence and global asymptotic stability of positive pseudo almost periodic solutions are established by using the fixed point method and the properties of pseudo almost periodic functions, together with constructing a suitable Lyapunov function. Finally, we present an example with simulations to support the theoretical results. The obtained results are essentially new and they extend previously known results. [ABSTRACT FROM AUTHOR]

In this paper, we consider the following Emden-Fowler type dynamic equations on time scales a(t)|xΔ (t)|a sgn xΔ(t)) Δ + b(t)|x(t)|β sgn x(t) = 0, when α < β. The classification of the nonoscillatory solutions are investigated and some necessary and sufficient conditions of the existence of oscillatory and nonoscillatory solutions are given by using the Schauder-Tychonoff fixed point theorem. Three possibilities of two classes of double integrals which are not only related to the co-efficients of the equation but also linked with the classification of the nonoscillatory solutions and oscillation of solutions are put forward. Moreover, an important property of the intermediate solutions on time scales is indicated. At last, an example is given to illustrate our main results. [ABSTRACT FROM AUTHOR]

In this present paper, we introduce a new measure of noncompactness on the space consisting of all real functions which are n times bounded and continuously differentiable on ℝ+. As an application, we investigate the problem of the existence of solutions for some classes of the functional integral-differential equations which enables us to study the existence of solutions of nonlinear integro-differential equations. In our considerations we apply the technique of measures of noncompactness in conjunction with Darbo's fixed point theorem. Finally, we give some illustrative examples to verify the effectiveness and applicability of our results. [ABSTRACT FROM AUTHOR]

The present paper is devoted to the existence of solutions for implicit first order differential systems with nonlocal conditions expressed by continuous linear functionals. The lack of complete continuity of the associated integral operators, due to the implicit form of the equations, is overcome by using Krasnoselskii's fixed point theorem for the sum of two operators. Moreover, a vectorial version of Krasnoselskii's theorem and the technique based on vector-valued norms and matrices having the spectral radius less than one are likely to allow the system nonlinearities to behave independently as much as possible. In addition, the connection between the support of the nonlocal conditions and the constants from the growth conditions is highlighted. [ABSTRACT FROM AUTHOR]

In this paper, using the Fourier series expansion and fixed point methods, we investigate the existence and uniqueness of Besicovitch almost periodic solutions for a class of second order differential equations involving reflection of the argument. Lipschitz nonlinear case is considered. [ABSTRACT FROM AUTHOR]

The aim of this paper is to discuss some basic problems (existence and uniqueness, data dependence) of the fixed point theory for a functional differential equation with an abstract Volterra operator. In the end an application is given. [ABSTRACT FROM AUTHOR]