Search

In this research, we will study the existence of weak solutions for a class of implicit elliptic equations involving the p-Laplace operator. Using a Krasnoselskii-Schaefer type theorem we establish our result, extending and complementing those obtained by R. Precup, 2020, and Marino and Paratore, 2021. [ABSTRACT FROM AUTHOR]

We use a variant of Krasnoselskii's fixed point theorem to show that the nonlinear difference equation with functional delay Δx (t) = - a (t) g (x (t)) + c (t)Δx(t_τ(t)) + q (t, x(t), x(t_τ(t))), has periodic solutions. For that end, we invert this equation to construct a fixed point mapping written as a sum of a completely continuous map and a large contraction which is suitable for the application of Krasnoselskii-Burton's theorem.

The purpose of this paper is to extend Krasnoselskii's fixed point theorem to the case of generalized Banach spaces for singlevalued and multivalued operators. As applications, we will give some existence results for abstract system of Fredholm-Volterra type differential equations and inclusions.

A famous dominated compactness theorem due to Krasnosel’skiĭ states that compactness of a regular linear integral operator in L p follows from that of a majorant operator. This theorem is extended to the case of the spaces $$L^{p(\cdot)}(\Omega, \mu, \varrho), \mu \Omega < \infty$$ , with variable exponent p(·), where we also admit power type weights $$\varrho$$ . This extension is obtained as a corollary to a more general similar dominated compactness theorem for arbitrary Banach function spaces for which the dual and associate spaces coincide. The result on compactness in the spaces $$L^{p(\cdot)}(\Omega, \mu, \varrho)$$ is applied to fractional integral operators over bounded open sets. [ABSTRACT FROM AUTHOR]

Abstract: This work deals with the existence and symmetry of positive solutions for a Neumann boundary value problem. It is a generalization of the work of Pedro J. Torres. The main result is the uniqueness of positive solutions, which is proved by an analytical method, for a given interval of the positive parameter . [Copyright &y& Elsevier]