Nontrivial solutions of boundary value problems for second order functional differential equations

In this paper we present a theory for the existence of multiple nontrivial solutions for a class of perturbed Hammerstein integral equations. Our methodology, rather than to work directly in cones, is to utilize the theory of fixed point index on affine cones. This approach is fairly general and covers a class of nonlocal boundary value problems for functional differential equations. Some examples are given in order to illustrate our theoretical results.Comment: 19 pages, revised versio

Higher order functional discontinuous boundary value problems on the half-line

In this paper, we consider a discontinuous, fully nonlinear, higher-order equation on the half-line, together with functional boundary conditions, given by general continuous functions with dependence on the several derivatives and asymptotic information on the (n−1)th derivative of the unknown function. These functional conditions generalize the usual boundary data and allow other types of global assumptions on the unknown function and its derivatives, such as nonlocal, integro-differential, infinite multipoint, with maximum or minimum arguments, among others. Considering the half-line as the domain carries on a lack of compactness, which is overcome with the definition of a space of weighted functions and norms, and the equiconvergence at ∞. In the last section, an example illustrates the applicability of our main result

On positive solutions for second-order boundary value problems of functional differential equations

WOS: 000313825900048In this paper, by using Krasnoselskii fixed point theorem, we obtain sufficient conditions for the existence of at least one or two positive solutions of a second-order boundary value problem for a class of nonlinear functional differential equations. Examples are also included to illustrate our results. (C) 2012 Elsevier Inc. All rights reserved