TOPOLOGICAL
DEGREE METHOD IN
HYBERBOLIC PROBLEMS
Wilson Yoshihiro AKASHI[1]
Célia Petil MILLER[2]
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ABSTRACT: This paper is concerned
with the study of existence of solutions for abstract equation of the form Lu =
Nu in Hilbert spaces, with L a linear operator not necessarily of Fredholm type
and N a nonlinear operator. The method used is based on fixed point theorems
via topological degree. As an application, we consider a nonlinear wave
equation and, under some conditions, we assure the existence of solutions for
this problem.
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KEYWORDS: Nonlinear wave
equations; fixed point theorems; topological degree.