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Multiple positive solutions for indefinite semilinear elliptic problems involving a critical Sobolev exponent

Published online by Cambridge University Press:  24 July 2014

Ching-yu Chen  and
Tsung-fang Wu
Ching-yu Chen
Affiliation:
Department of Applied Mathematics, National University of Kaohsiung, Kaohsiung 811, Taiwan, [email protected]
Tsung-fang Wu
Affiliation:
Department of Applied Mathematics, National University of Kaohsiung, Kaohsiung 811, Taiwan, [email protected]
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Abstract

In this paper, we study the decomposition of the Nehari manifold by exploiting the combination of concave and convex nonlinearities. The result is subsequently used, in conjunction with the Ljusternik–Schnirelmann category and variational methods, to prove the existence and multiplicity of positive solutions for an indefinite elliptic problem involving a critical Sobolev exponent.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 144 , Issue 4 , August 2014 , pp. 691 - 709
Copyright
Copyright © Royal Society of Edinburgh 2014 

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