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Existence and multiplicity of solutions for an indefinite Kirchhoff-type equation in bounded domains

Published online by Cambridge University Press:  03 March 2016

Juntao Sun
Affiliation:
School of Science, Shandong University of Technology, Zibo 255049, People’s Republic of China (sunjuntao2008@163.com)
Tsung-fang Wu
Affiliation:
Department of Applied Mathematics, National University of Kaohsiung, Kaohsiung 811, Taiwan (tfwu@nuk.edu.tw)

Abstract

We study the indefinite Kirchhoff-type problem where Ω is a smooth bounded domain in and . We require that f is sublinear at the origin and superlinear at infinity. Using the mountain pass theorem and Ekeland variational principle, we obtain the multiplicity of non-trivial non-negative solutions. We improve and extend some recent results in the literature.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 2016 

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