00 It x = S QnIf» m addition, the projections Pn = £ Q,are equicontinuous, then n = 1 « = 1 (£n)^°=1 is said to be an equi-Schauder decomposition of E. It is obvious that a Schauder basis is equivalent to a Schauder decomposition in which each subspace is one-dimensional, and that it is equi-Schauder if and only if the corresponding decomposition is equi-Schauder. For more information on Schaud...

This paper studies sufficient conditions for the existence of solutions to the problem of sequential derivatives of nonlinear qdifference equations with three-point q-integral boundary conditions. Our results are concerned with several quantum numbers of derivatives and integrals. By using Banach’s contraction mapping, Krasnoselskii’s fixed-point theorem, and Leray-Schauder degree theory, some ...

In this article, we discuss the existence as well as global attractivity and ultimate positivity of solutions for a certain nonlinear first order ordinary differential equation on the unbounded intervals of real line via a classical fixed point theorem of Schauder (Smart [12, page 15]). Our hypotheses and claims have also been explained with the help of two realizations under some natural condi...

The aim of this paper is to study the solvability of the Dirichlet problem for certain types of fully nonlinear elliptic equations. The theory of weakly-near operators, combined to Contraction Mapping and Schauder fixed point theorems, is used. Our main results generalizes similar ones given by S. Campanato and A. Tarsia.

We study the traveling waves of reaction-diffusion equations for a diffusive SIR model. The existence of traveling waves is determined by the basic reproduction number of the corresponding ordinary differential equations and the minimal wave speed. Our proof is based on Schauder fixed point theorem and Laplace transform.

In this paper, we shall discuss the properties of the well-known Mittag–Leffler function, and consider the existence of solution of the periodic boundary value problem for a fractional differential equation involving a Riemann–Liouville sequential fractional derivative by means of the method of upper and lower solutions and Schauder fixed point theorem.

In this paper, we present some alternative results concerning with the existence and attractivity dependence of solutions for a class of nonlinear fractional functional differential equations. In our consideration, we apply the well-known Schauder fixed point theorem in conjunction with the technique of measure of noncompactness. Moreover, we provide examples to illustrate the effectiveness of ...

In this paper, we investigate the existence of positive solutions for second-order nonlinear three-point integral boundary value problems. By using the Leray-Schauder fixed point theorem, some sufficient conditions for the existence of positive solutions are obtained, which improve the results of literature Tariboon and Sitthiwirattham [J. Tariboon, T. Sitthiwirattham, Boundary Value Problems, ...

In this paper, we study the existence of global solutions for a class of impulsive abstract functional differential equation with nonlocal conditions. The results are obtained by using the Leray-Schauder alternative fixed point theorem. An example is provided to illustrate the theory.

This article concerns a multi-dimensional Cahn-Hilliard equation subject to Neumann boundary condition. We show existence of the periodic solutions by using the viscosity approach. By applying the Schauder fixed point theorem, we show existence of the solutions to the suitable approximate problem and then obtain the solutions of the considered periodic problem using a priori estimates. Our resu...