The connectivity and compactness of solution set of an integral equation and weak solution set of an initial-boundary value problem.
https://doi.org/10.1515/dema-2006-0215Publisher, magazine: ,
Publication year: 2006
Lưu Trích dẫn Chia sẻAbstract
In this paper we show that the set of solutions to the following integral equation (1) (Equation presented) and that of weak solutions to the initial-boundary value problem for the following semilinear wave equation are nonempty, connected and compact (Equation presented), where u0, u1, f are given functions, the unknown function u(x, t) and the unknown boundary value P(t) satisfy the following nonlinear integral equation (Equation presented) where g, H, k are given functions. The main tool is the topological degree theory of compact vector fields.
Tags: nonlinear integral equation; weak solution; topological degree; compact vector fields; relatively compact set; initial boundary value problem; semilinear wave equation
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