Bifurcation problems associated with generalized Laplacians
Klaus Schmitt, Inbo Sim · Advances in Differential Equations · 2004
This paper is concerned with bifurcation problems for nonlinear partial differential equations of the form $$-\mbox{div}(a(| abla u|) abla u) = \lambda g(u)$$ 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.