Abstract
This survey paper presents the new method worked out in [14] and [15] 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.
Authors
Radu Precup
Department of Mathematics Babes-Bolyai University, Cluj-Napoca, Romania
Keywords
positive solution; cone; fixed point; wave equation
Paper coordinates
R. Precup, Existence and localization results for semi-linear problems, Annals Univ. Craiova, Math. Comp. Sci. Ser. 32 (2005), 59-66.
About this paper
Journal
Annals of University of Craiova, Math. Comp. Sci. Ser.
Publisher Name
journal paper website
Print ISSN
1223-6934
Online ISSN
MR, ZBL
MR2215896,
google scholar link
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