On the global structure of the set of positive solutions for some quasilinear elliptic boundary value problems (Q5953921)

This paper deals with the study of the structure of positive solutions of NEWLINE\[NEWLINE\begin{cases} -\text{div} \bigl(|Du|^{p-2} Du\bigr)=\lambda f(u) \quad &\text{in }\Omega\\ u=0\quad &\text{on }\partial\Omega,\end{cases} \tag{1}NEWLINE\]NEWLINE where \(p>1\), \(\Omega\) is a bounded smooth domain of \(\mathbb{R}^N\), \(N\geq 1\) and nonlinearity \(f\) satisfies some natural assumptions. Under some ``monotonicity'' assumption on \(f\) the authors prove existence of at most one positive solution of (1), that is a uniqueness result.