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Nodal solutions of a p-Laplacian equation

Published online by Cambridge University Press:  22 June 2005

Thomas Bartsch ,
Zhaoli Liu  and
Tobias Weth
Thomas Bartsch
Affiliation:
Mathematisches Institut, Universität Giessen, Arndtstrasse 2, 35392 Giessen, Germany. E-mail: Thomas.Bartsch@math.uni-giessen.de, Tobias.Weth@math.uni-giessen.de
Zhaoli Liu
Affiliation:
Department of Mathematics, Capital Normal University, Beijing 100037, P. R. China. E-mail: zliu@mail.cnu.edu.cn
Tobias Weth
Affiliation:
Mathematisches Institut, Universität Giessen, Arndtstrasse 2, 35392 Giessen, Germany. E-mail: Thomas.Bartsch@math.uni-giessen.de, Tobias.Weth@math.uni-giessen.de
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Abstract

We prove that the $p$-Laplacian problem $-\Delta_p u = f(x, u)$, with $u \in W^{1, p}_0 (\Omega)$ on a bounded domain $\Omega \subset R^N$, with $p > 1$ arbitrary, has a nodal solution provided that $f : \Omega \times R \to R$ is subcritical, and $f(x, t) / |t|^{p - 2}$ is superlinear. Infinitely many nodal solutions are obtained if, in addition, $f(x, -t) = -f(x, t)$.

Keywords

p-Laplacian equationsuperlinear non-linearitynodal solutionvariational methodinvariant set of descending flow35J2035J6558E05
Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 91 , Issue 1 , July 2005 , pp. 129 - 152
Copyright
2005 London Mathematical Society

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