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A Topological and Geometric Approach to Fixed Points Results for Sum of Operators and Applications

Cleon S. Barroso·Eduardo V. Teixeira
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Abstract

In the present paper we establish a fixed point result of Krasnoselskii type for the sum $A+B$, where $A$ and $B$ are continuous maps acting on locally convex spaces. Our results extend previous ones. We apply such results to obtain strong solutions for some quasi-linear elliptic equations with lack of compactness. We also provide an application to the existence and regularity theory of solutions to a nonlinear integral equation modeled in a Banach space. In the last section we develop a sequentially weak continuity result for a class of operators acting on vector-valued Lebesgue spaces. Such a result is used together with a geometric condition as the main tool to provide an existence theory for nonlinear integral equations in $L\sp p(E)$.

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Cleon S. Barroso, Eduardo V. Teixeira. 2004-08-09. A Topological and Geometric Approach to Fixed Points Results for Sum of Operators and Applications. https://arxiv.org/abs/math/0403474

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