Alternative Of Leray-Schauder Research Articles

REFE-Acceptable Mappings: Necessary and Sufficient Condition for the Nonexistence of a Regular Exceptional Family of Elements

By considering the notion of regular exceptional family of elements (REFE), we define the class of REFE-acceptable mappings. By definition, a complementarity problem on a Hilbert space defined by a REFE-acceptable mapping and a closed convex cone has either a solution or a REFE. We present several classes of REFE-acceptable mappings. For this, neither the topological degree nor the Leray-Schauder alternative is necessary. By using the concept of REFE-acceptable mappings, we present necessary and sufficient conditions for the nonexistence of regular exceptional family of elements. These conditions are used for generating several existence theorems and existence and uniqueness theorems for complementarity problems.

Periodic boundary value problem for first-order impulsive functional differential equations

This paper discusses the periodic boundary value problem for a class of first-order impulsive functional differential equations. We establish several existence results under weaker hypotheses by using the Leray–Schauder alternative, the lower and upper solution method and the monotone iterative technique. The corresponding results in the literature are improved or extended, some examples are also given to illustrate the advantage of the results.

Nonlinear integral equations singular in the dependent variable

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.

An Upper and Lower Solution Theory for the Problem (G'(y))' + f(t, y) = 0 on Finite and Infinite Intervals

A new upper and lower solution theory is presented for the second order problem (G'(y))' + f(t, y) = 0 on finite and infinite intervals. The theory on finite intervals is based on a Leray–Schauder alternative, whereas the theory on infinite intervals is based on results on the finite interval and a diagonalization process.

A Leray-Schauder alternative for weakly-strongly sequentially continuous weakly compact maps

AbstractA new applicable Leray-Schauder alternative is presented for weakly-strongly sequentially continuous maps. This result is then used to establish a general existence principle for operator equations.

Antiperiodic boundary value problem for first-order impulsive ordinary differential equations

This paper discusses the antiperiodic boundary value problem for first-order impulsive ordinary differential equations. We establish several existence results by using the Leray-Schauder alternative, the lower and upper solution method and the monotone iterative technique.

Analytic solutions to integral equations in the complex domain

Schauder's fixed point theorem and the Leray–Schauder alternative are used to establish the existence of analytic solutions to integral equations in the complex domain.

Existence results for partial neutral functional integrodifferential equations with unbounded delay

We prove the existence of mild solutions for a partial neutral functional integrodifferential equation with unbounded delay using the Leray–Schauder alternative.

On the existence and uniqueness of solutions to boundary value problems on time scales

This work formulates existence, uniqueness, and uniqueness-implies-existence theorems for solutions to two-point vector boundary value problems on time scales. The methods used include maximum principles, a priori bounds on solutions, and the nonlinear alternative of Leray-Schauder.

Controllability of second-order semilinear neutral functional differential systems in Banach spaces

Sufficient conditions for controllability of semilinear second-order neutral functional differential systems in Banach spaces are established using the theory of strongly continuous cosine families. The results are obtained by using the Leray-Schauder alternative.

GLOBAL EXISTENCE OF SOLUTIONS OF CERTAIN HIGHER ORDER DIFFERENTIAL EQUATIONS

In this paper global existence results for certain higher order differential equations are established. Our analysis is based on a simple and classical application of the Leray-Schauder alternative.

Periodic boundary value problems for nonlinear first order ordinary differential equations

We prove several new existence results for a nonlinear anti-periodic first order problem using a Leray-Schauder alternative. Two definitions of lower and upper solutions are presented and we show in this paper the validity of the lower and upper solution method. Also, we give a method to generate a sequence of approximate solutions converging to a solution of the anti-periodic problem. ∗First and second authors were supported in part by D.G.E.S.I.C. (Spain), project PB97 – 0552. †This is the preprint version of the paper published in Journal of Mathematical Inequalities and Applications, Vol. 6 (2003) 477–485. ‡Corresponding author

Boundary value problems for second and higher order differential equations

In this paper the nonlinear alternative of Leray-Schauder is used to obtain existence results for second and higher order boundary value problems.