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

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Malekzadeh, Soheil | 2011

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 41880 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Ranjbar, Ali
Abstract:
In this thesis, 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. 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. Finally, 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 Lp(E)
Keywords:
Krasnoselski Fixed Point Theorem ; Locally Convex Spaces ; Quasi-Linear Elliptic Equation ; Regularity Theory ; Nonlinear Integral Equation