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Bifurcation points of a degenerate elliptic boundary-value problem
We consider the nonlinear elliptic eigenvalue problem \begin{align*} -\nabla\cdot\{A(x)\nabla u(x)\} & =\lambda f(u(x))\text{ for }x\in\Omega\\ u(x) & =0\text{ for }x\in\partial\Omega \end{align*} where \Omega is a bounded open subset of \mathbb{R}^{N} and f\in C^{1}(\mathbb{R}) with f(0)=0 and f^{\prime}(0)=1 . The ellipticity is degenerate in the sense that 0\in\Omega and A(x)>0 for …