S.K. Ntouyas

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

On First Order Impulsive Dynamic Equations on Time Scales

In this paper, the nonlinear alternative of Leray-Schauder type is used to investigate the existence of solutions for first order impulsive dynamic equations on time scales.

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.

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.

Nondensely defined evolution impulsive differential inclusions with nonlocal conditions

In this paper, we shall establish sufficient conditions for the existence of integral solutions for some nondensely defined evolution impulsive differential inclusions in Banach spaces with nonlocal conditions.

Positive solutions of the three-point boundary value problem for fractional-order differential equations with an advanced argument

AbstractIn this article, we consider the existence of at least one positive solution to the three-point boundary value problem for nonlinear fractional-order differential equation with an advanced argument where 2 < α ≤ 3, 0 < η < 1, , CDα is the Caputo fractional derivative. Using the well-known Guo-Krasnoselskii fixed point theorem, sufficient conditions for the existence of at least one positive solution are established. MSC (2010): 34A08; 34B18; 34K37.

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.

Controllability Results for Nondensely Defined Semilinear Functional Differential Equations

In this paper we investigate the controllability of first order semilinear functional and neutral functional differential equations in Banach spaces.

Controllability Results for Evolution Inclusions with Non-Local Conditions

In this paper we prove controllability results for mild solutions defined on a compact real interval for first order differential evolution inclusions in Banach spaces with non-local conditions. By using suitable fixed point theorems we study the case when the multi-valued map has convex as well as non-convex values.

Eigenvalue Problems for Systems of Nonlinear Boundary Value Problems on Time Scales

Values of λ are determined for which there exist positive solutions of the system of dynamic equations, , , for , satisfying the boundary conditions, , where is a time scale. A Guo-Krasnoselskii fixed point-theorem is applied.