This survey paper presents the new method worked out in  and  for the existence and localization of solutions to evolution operator equations, which is based on Krasnoselskii’s compression-expansion fixed point theorem in cones. The main idea is to handle two equivalent operator forms of the equation, one of fixed point type giving the operator to which Krasnoselskii’s theorem applies and an other one of coincidence type which is used to localize a positive solution in a shell. Applications are presented for a boundary value problem associated to a fourth order partial differential equation on a rectangular domain and for nonlinear wave equations.
Department of Mathematics Babes-Bolyai University, Cluj-Napoca, Romania
positive solution; cone; fixed point; wave equation
R. Precup, Existence and localization results for semi-linear problems, Annals Univ. Craiova, Math. Comp. Sci. Ser. 32 (2005), 59-66.
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Annals of University of Craiova, Math. Comp. Sci. Ser.
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