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February 2010 Multiple Solutions for Noncoercive Problems with the $p$-Laplacian
Leszek Gasiński, Nikolaos S. Papageorgiou
Bull. Belg. Math. Soc. Simon Stevin 17(1): 83-99 (February 2010). DOI: 10.36045/bbms/1267798500

Abstract

We consider a nonlinear elliptic equation driven by the $p$-Laplacian and with a Carathéodory right hand side nonlinearity which exhibits an asymmetric asymptotic behaviour at $+\infty$ and at $-\infty$. These hypotheses imply that the Euler functional of the problem is noncoercive (indefinite). Using critical point theory, we prove the existence of at least two nontrivial smooth solutions. Also in the last section for the asymmetric functionals considered here, we compute the critical groups at infinity.

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Leszek Gasiński. Nikolaos S. Papageorgiou. "Multiple Solutions for Noncoercive Problems with the $p$-Laplacian." Bull. Belg. Math. Soc. Simon Stevin 17 (1) 83 - 99, February 2010. https://doi.org/10.36045/bbms/1267798500

Information

Published: February 2010
First available in Project Euclid: 5 March 2010

zbMATH: 1185.35079
MathSciNet: MR2656673
Digital Object Identifier: 10.36045/bbms/1267798500

Subjects:
Primary: 35J65 , 58E05

Keywords: $p$-Laplacian , critical groups , multiple solutions , noncoercive functional , Poincaré-Hopf formula , Principal eigenvalue

Rights: Copyright © 2010 The Belgian Mathematical Society

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Vol.17 • No. 1 • February 2010
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