Bifurcation of positive solutions from zero or infinity in elliptic problems which are not linearizable (Q5931371)

The authors consider the boundary-value problem NEWLINE\[NEWLINE-\sum^m_{i,j=1} {\partial\over\partial x_i} \Biggl(a_{ij} {\partial u\over\partial x_j}\Biggr)+ b\cdot u= \lambda a\cdot u+ h(\cdot,u,\nabla u,\lambda)\quad\text{in }\Omega,NEWLINE\]NEWLINE NEWLINE\[NEWLINEu= 0\quad\text{on }\partial\Omega.NEWLINE\]NEWLINE Where \(\Omega\) is a bounded domain in \(\mathbb{R}^m\) \((m>1)\) with smooth boundary \(\partial\Omega\), \(\lambda\in \mathbb{R}^1\), \(a_{ij}\in C^1(\overline\Omega)\), and \(a,b\in C^0(\overline\Omega)\). The function \(h\in (\overline\Omega\times \mathbb{R}^1\times \mathbb{R}^m\times\mathbb{R}^1, \mathbb{R}^1)\) is assumed to be continuous and have a special form.