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2004 Bifurcation problems associated with generalized Laplacians
Klaus Schmitt, Inbo Sim
Adv. Differential Equations 9(7-8): 797-828 (2004).

Abstract

This paper is concerned with bifurcation problems for nonlinear partial differential equations of the form $$-\mbox{div}(a(|\nabla u|)\nabla u) = \lambda g(u)$$ which are subject to Dirichlet boundary conditions. We show the existence of infinitely many nontrivial solutions of the eigenvalue problems in the case where $a(|t|) = |t|^{p-2}$ and $g(t) = |t|^{p-2}t, $ $p> 1.$ More general situations are also considered.

Citation

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Klaus Schmitt. Inbo Sim. "Bifurcation problems associated with generalized Laplacians." Adv. Differential Equations 9 (7-8) 797 - 828, 2004.

Information

Published: 2004
First available in Project Euclid: 18 December 2012

zbMATH: 1220.35053
MathSciNet: MR2100396

Subjects:
Primary: 35J60
Secondary: 35B32, 35B45, 35B65, 47J15

Rights: Copyright © 2004 Khayyam Publishing, Inc.

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Vol.9 • No. 7-8 • 2004
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