In this paper, the Leray-Schauder Alternative is used to investigate the existence of mild solutions to first-order nonlinear functional integrodifferential evolution equations with nonlocal conditions in Banach spaces. AMS subject classifications: 34K30, 34A60, 34G20

This paper deals with the existence of solutions to some classes of partial impulsive hyperbolic differential inclusions with variable times involving the Caputo fractional derivative. Our works will be considered by using the nonlinear alternative of Leray-Schauder type.

Nonnegative solutions are established for nonlinear integral equations where the nonlinearity G(t, y) may be singular at y = 0. Existence is established using the Leray–Schauder alternative. c © 2007 Elsevier Ltd. All rights reserved.

In this paper, by employing fixed point index theory and Leray-Schauder degree theory, we obtain the existence and multiplicity of sign-changing solutions for nonlinear second-order differential equations with integral boundary value conditions.

In this paper we present some criteria for Φ-essential maps and as a consequence these generate a number of new Leray-Schauder type alternatives. c ©2016 All rights reserved.

Here is established the global existence of smooth solutions to a generalized nonlinear equation of Schrödinger type in the usual Sobolev spaces H and certain weighted Sobolev spaces by using Leray-Schauder fixed point theorem and delicate a priori estimates.

The Banach fixed point theorem and the nonlinear alternative of Leray–Schauder type are used to investigate the existence of solutions for fractional order functional and neutral functional differential equations with infinite delay. © 2007 Elsevier Inc. All rights reserved.

We give an existence result for a periodic boundary value problem involving mean curvaturelike operators in the scalar case. Following [3], we use an approach based on the Leray-Schauder degree.

Sufficient conditions for controllability of neutral functional integrodifferential systems in Banach spaces with initial condition in the phase space are established. The results are obtained by using the Schauder fixed point theorem. An example is provided to illustrate the theory.

In this paper, sufficient conditions are given for the existence of solutions for a class of second order stochastic differential inclusions in Hilbert space with the help of Leray-Schauder Nonlinear Alternative.