Existence theory for nonlinear operator equations of Hammerstein type in Banach spaces
AbstractWe use topological methods to develop an existence theory for nonlinear operator equations of Hammerstein type in Banach spaces. In…
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Positive solutions of evolution operator equations
AbstractExistence and localization results are derived from Krasnoselskii’s compressionexpansion fixed point theorem in cones, for operator equations in spaces of…
Nonnegative solutions of nonlinear integral equations in ordered Banach spaces
AbstractThe main purpose of this paper is to make Krasnoselskii’s compression-expansion fixed point theorem applicable to nonlinear integral equations in…
A note on the solvability of the nonlinear wave equation
AbstractNew existence and localization results for the nonlinear wave equation are established by means of the Schauder fixed point theorem.…
Continuation theory for general contractions in gauge spaces
AbstractA continuation principle of Leray-Schauder type is presented for contractions with respect to a gauge structure depending on the homotopy…
On the continuation principle for nonexpansive maps
Abstract In this note the continuation principle (nonlinear alternative) for nonexpansive maps on Hilbert spaces (see [5]) in extended in…
Monotone technique to the initial values problem for a delay integral equation from biomathematics
Abstract We present a constructive method for solving (1)-(2) under hypotheses (i)-(iv) by assuming that function \(f(t,x)\) is monotone with…
Existence and localization results for the nonlinear wave equation
Abstract Existence and localization results for the nonlinear wave equation are established by Krasnoselskii’s compression-expansion fixed point theorem in cones.…
Anti-periodic solutions for second order differential inclusions
Abstract In this paper, we extend the existence results presented in [9] for \(L^p\) spaces to operator inclusions of Hammerstein…
Fixed point theory and generalized Leray-Schauder alternatives for approximable maps in topological vector spaces
AbstractSome new fixed point theorems for approximable maps are obtained in this paper. Homotopy results, via essential maps, are also…