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Existence and structure of the set of positive solutions of a general class of sublinear elliptic non-classical mixed boundary value problems. (English) Zbl 1142.35509
This paper is devoted to the study of the existence of positive solutions of the sublinear weighted elliptic mixed boundary value problem $\begin{gathered} Lu=\lambda W(x)u- a(x) f(x,u)u\quad\text{in }\Omega,\\ {\mathcal B}(b)u= 0\quad\text{on }\partial\Omega,\end{gathered}\tag{1}$ 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 $$a(x)$$.

##### MSC:
 35L65 Hyperbolic conservation laws 35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs 47J15 Abstract bifurcation theory involving nonlinear operators
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