### Bifurcation problems associated with generalized Laplacians

#### 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.

#### Article information

Source
Adv. Differential Equations Volume 9, Number 7-8 (2004), 797-828.

Dates
First available in Project Euclid: 18 December 2012