Existence of solutions for p(x)-Kirchhoff type problems with non-smooth potentials

We consider a class of p(x)-Kirchhoff type problem with a subdifferential term and a discontinuous perturbation. Assuming the existence of an ordered pair of appropriately defined upper and lower solutions, by the method of lower-upper solutions, penalization techniques, truncations, and results fro...

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Bibliographic Details
Published inElectronic journal of differential equations Vol. 2015; no. 193; pp. 1 - 18
Main Authors Ziqing Yuan, Lihong Huang
Format Journal Article
LanguageEnglish
Published Texas State University 22.07.2015
Subjects
Extremal solutions
fixed point
p(x)-Kirchhoff type problem
upper and lower solutions
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Summary:We consider a class of p(x)-Kirchhoff type problem with a subdifferential term and a discontinuous perturbation. Assuming the existence of an ordered pair of appropriately defined upper and lower solutions, by the method of lower-upper solutions, penalization techniques, truncations, and results from nonlinear and multivalued analysis, we show the existence of solutions, and of extremal solutions in the interval defined by the lower and upper solution.
ISSN:1072-6691