GLOBAL BIFURCATION FOR GENERALIZED LAPLACIAN OPERATORS

Title & Authors
GLOBAL BIFURCATION FOR GENERALIZED LAPLACIAN OPERATORS
Kim, In-Sook;

Abstract
A bifurcation problem for nonlinear partial differential equations of the form $\small{div({\varphi}(|{\nabla}u|){\nabla}u+{\mu}_0{\varphi}(|u|)u=q({\lambda},\;x,\;u,\;{\nabla}u)}$ subject to Dirichlet boundary conditions is discussed. Using a global bifurcation theorem of Rabinowitz type, we show that under certain conditions on $\small{\varphi}$ and q, the above equation has an unbounded connected set of solutions (u, $\small{\lambda}$).
Keywords
bifurcation;generalized Laplacian;unbounded component;
Language
English
Cited by
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