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Multiple solutions for elliptic resonant problems

Published online by Cambridge University Press:  12 November 2008

Shibo Liu
Shibo Liu
Affiliation:
Department of Mathematics, Xiamen University, Xiamen 361005, People's Republic of China
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Abstract

Two non-trivial solutions for semilinear elliptic resonant problems are obtained via the Lyapunov—Schmidt reduction and the three-critical-points theorem. The difficulty that the variational functional does not satisfy the Palais—Smale condition is overcome by taking advantage of the reduction and a careful analysis of the reduced functional.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 138 , Issue 6 , December 2008 , pp. 1281 - 1289
Copyright
Copyright © Royal Society of Edinburgh 2008

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