Existence and structure of the set of positive solutions of a general class of sublinear elliptic non-classical mixed boundary value problems. (Q5960814)

This paper is devoted to the study of the existence of positive solutions of the sublinear weighted elliptic mixed boundary value problem NEWLINE\[NEWLINE\begin{gathered} Lu=\lambda W(x)u- a(x) f(x,u)u\quad\text{in }\Omega,\\ {\mathcal B}(b)u= 0\quad\text{on }\partial\Omega,\end{gathered}\tag{1}NEWLINE\]NEWLINE where \(a(x)\in L^\infty(\Omega)\), \(a(x)\geq 0\) and \(W\in L^\infty(\Omega)\). The author analyses the structure of the diagram of positive solutions of (1), accordingly to the sign of potential \(W\) in the vanishing set of \(a(x)\).