P. Ch. Tsamatos

On an m -point boundary-value problem for second-order ordinary differential equations

where q E (0, 1) is given. We obtain conditions for the existence and uniqueness of a solution for the boundary-value problem (2), using the Leray-Schauder continuation theorem [2]. We give an example of a three-point boundary-value problem where the existence condition is not satisfied and no solution exists. Gupta [3] recently studied the boundary-value problem (2) when Q! = 1. Our results on the three-point boundary-value problem (2) extend the results of Gupta [3], to the case of general CY. (See also [4, 51.) We use the classical spaces C[O, 11, C’[O, 11, Lk[O, 11, and L”[O, l] of continuous, k-times continuously differentiable, measurable real-valued functions whose kth power of the absolute value is Lebesgue integrable on [0, 11, or measurable functions that are essentially bounded

Global existence for semilinear evolution integrodifferential equations with delay and nonlocal conditions

In this paper, we study the global existence of solutions for semilinear evolution integrodifferential equations with nonlocal conditions, via a fixed point analysis approach. Using the Leray-Schauder Alternative, we derive conditions under which a solution exists globally.

Sufficient conditions for the existence of nonnegative solutions of a nonlocal boundary value problem

Abstract In this paper, we provide sufficient conditions for the existence of nonnegative solutions of a nonlocal boundary value problem for a second-order ordinary differential equation. By applying Krasnoselskiis fixed-point theorem in a cone, first we prove the existence of solutions of an auxiliary BVP formulated by truncating the response function. Then the Arzela-Ascoli Theorem is used to take C 1 limits of sequences of such solutions.

Globsl existence for second order semilinear ordinary and delay integrodifferential equations with nonlocal conditions

In this paper, we study the global existence of solutions for second order intial problems, with nonlocal conditions, for semilinear ordinary and delay integrodifferential equations, by using the Leray-Schauder Alternative.

Multiple positive solutions for a functional second-order boundary value problem

By using the Krasnoselskii fixed point theorem on cones in Banach spaces some existence results of positive solutions of a boundary value problem concerning a second-order functional differential equation are given.

Global existence for functional integro-differential equations of delay and neutral type

In this paper, we studt the global existence of solutions for initial value problems for funtional integro—differential equatios of dalay and neutral type. Using the leray—Schauder Alternative, we derive conditions under which a solutiosn exists globally.

Global solutions of a singular initial value problem to second order nonlinear delay differential equations

The paper is concerned with an initial value problem to second order nonlinear singular delay differential equations. By the use of the Schauder fixed point theorem, a result for the existence of global solutions is derived. Also, via the Banach contraction principle, another result concerning the existence and uniqueness of global solutions is established. Moreover, applications of these results to a particular case of second order nonlinear singular delay differential equations as well as to the special case of second order nonlinear singular ordinary differential equations are presented. Finally, some specific applications to certain equations and two examples are given to demonstrate the applicability of the results of the paper.

Triple solutions for a nonlocal functional boundary value problem by leggett–williams theorem

The existence of triple solutions for a second-order nonlocal functional boundary value problem is proved by using a fixed-point theorem on cones in Banach spaces due to Leggett and Williams. The obtained results are new even in the ordinary case for three-point boundary value problems discussed quite recently in [Xiaoming He and Weigao Ge (2002). Triple solutions for second-order three-point boundary value problems. J. Math. Anal. Appl., 268, 256–265].

Global existence for second order functional semilinear equations

In this paper we study the global existence of solutions for initial value problems for functional semilinear equations, where the linear operator in the differential equation is the infinitesimal generator of a strongly cosine family in a Banach spaceX. Using the Leray-Schauder Alternative, we derive conditions under which a solution exists globally.

Global Existence for Functional Semilinear Volterra Integrodifferential Equations in Banach Spaces

In this paper, we study the global existence of solutions for initial value problems for functional semilinear Volterra integrodifferential equations in a Banach space, by using the Leray-Schauder Alternative.