We study the classes of homogeneous polynomials on a Banach space with unconditional Schauder basis that have unconditionally convergent monomial expansions relative to this basis. We extend some results of Matos, and we show that the homogeneous polynomials with unconditionally convergent expansions coincide with the polynomials that are regular with respect to the Banach lattices structure of...

By virtue of the upper and lower solutions method, as well as the Schauder fixed point theorem, the existence of positive solutions to a class of q-fractional difference boundary value problems with φ-Laplacian operator is investigated. The conclusions here extend existing results. c ©2016 All rights reserved.

We study a model for three cyclically coupled neurons with eventually negative delayed feedback, and without symmetry or monotonicity properties. Periodic solutions are obtained from the Schauder fixed point theorem. It turns out that, contrary to lower dimensional cases, instability at zero does not exclude monotonously decaying solutions.

Abstract. In this paper, we study the global existence of classical solutions for the Cahn-Hilliard equation with terms of lower order and non-constant mobility. Based on the Schauder type estimates, under some assumptions on the mobility and terms of lower order, we establish the global existence of classical solutions.

This paper studies a new class of nonlocal boundary value problems of nonlinear differential equations and inclusions of fractional order with fractional integral boundary conditions. Some new existence results are obtained by using standard fixed point theorems and Leray-Schauder degree theory. Some illustrative examples are also discussed.

The purpose of this article is to introduce the notion of cone valued measure of noncompactness. Our theoretical approach generalizes recent results for cone measure of noncompactness. For the proofs of our results we use the famous Schauder-Tichonov Theorem as well as Robert Cauty theorem in the new framework.

Recommended by Colin Rogers We establish the existence of multiple positive solutions for a singular nonlinear third-order periodic boundary value problem. We are mainly interested in the semipositone case. The proof relies on a nonlinear alternative principle of Leray-Schauder, together with a truncation technique.

In this paper, we study positive periodic solutions to singular second order differential systems. It is proved that such a problem has at least two positive periodic solutions. The proof relies on a nonlinear alternative of Leray–Schauder type and on Krasnosel’skĭı fixed point theorem on compression and expansion of cones.

A system of higher-order nonlinear fractional differential equations is studied in this article, and some sufficient conditions for existence and uniqueness of a solution for the system is established by the nonlinear alternative of Leray-Schauder and Banach contraction principle.

This paper is devoted to the study of the existence and uniqueness of the positive solution for a type of the nonlinear third-order three-point boundary value problem. Our results are based on an iterative method and the Leray-Schauder fixed point theorem.