Journal of the
Korean Mathematical Society JKMS

A bifurcation problem for nonlinear partial differential equations of the form $$ \mbox{div}(\varphi(|\triangledown u|)\triangledown u+\mu_0 \varphi(|u|)u= q(\lambda,x,u, \triangledown u)$$ 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

MSC numbers: 47J05, 47J10, 34B15