On the structure of solutions of a class of boundary value problems (Q2716470)

The authors deal with the following problem: NEWLINE\[NEWLINE\begin{cases} -\Delta u=\lambda u^q+u^p, & x\in\Omega,\\ u>0, & x\in\Omega,\\ u=0, & x\in\partial \Omega \end{cases}NEWLINE\]NEWLINE with \(0<q<1<p\). The main feature is the presence of a nonlinearity having a sublinear and superlinear behaviour. Using topological methods on cones the authors show the existence of a branch \(C_{0,0}\) of solutions bifurcating from \((0,0)\).