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http://dx.doi.org/10.4134/JKMS.2009.46.1.031

GLOBAL BIFURCATION FOR GENERALIZED LAPLACIAN OPERATORS  

Kim, In-Sook (DEPARTMENT OF MATHEMATICS SUNGKYUNKWAN UNIVERSITY)
Publication Information
Journal of the Korean Mathematical Society / v.46, no.1, 2009 , pp. 31-39 More about this Journal
Abstract
A bifurcation problem for nonlinear partial differential equations of the form $$div({\varphi}(|{\nabla}u|){\nabla}u+{\mu}_0{\varphi}(|u|)u=q({\lambda},\;x,\;u,\;{\nabla}u)$$ subject to Dirichlet boundary conditions is discussed. Using a global bifurcation theorem of Rabinowitz type, we show that under certain conditions on $\varphi$ and q, the above equation has an unbounded connected set of solutions (u, $\lambda$).
Keywords
bifurcation; generalized Laplacian; unbounded component;
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