Journal Home Page Cumulative Index List of all Volumes Complete Contentsof this Volume Previous Article Minimax Theory and its Applications 04 (2019), No. 1, 021--032Copyright Heldermann Verlag 2019 A Multiplicity Result for a Non-Autonomous Sublinear Elliptic Problem Involving Nonlinearities Indefinite in Sign Giovanni Anello Dept. of Mathematical and Computer Science, University of Messina, Viale F. Stagno d'Alcontres 31, 98166 Messina, Italy ganello@unime.it Luca Furnari Dept. of Mathematical and Computer Science, University of Messina, Viale F. Stagno d'Alcontres 31, 98166 Messina, Italy lfurnari@unime.it [Abstract-pdf] \newcommand{\R}{{\mathbb R}} Let $\Omega$ be a bounded smooth domain in $\R^N$, let $\alpha,\beta \colon \Omega \rightarrow \R$ be two measurable functions, and let $s\in ]1,2[$ and $r\in ]1,s[$. We deal with the following non autonomous elliptic problem \begin{equation*} \left\{ \begin{aligned} & - \Delta u=\alpha(x)u^{s-1}-\mu \beta(x) u^{r-1}, \ \ \ &&{\rm in}\ \ \Omega\\ & u\geq 0, &&{\rm in}\ \ \Omega\\ & u_{\mid \partial \Omega}=0 \end{aligned} \right. \end{equation*} where $\mu\in \R$ is a parameter. We establish, via minimax methods, a multiplicity result under suitable summability conditions on the weight functions $\alpha,\beta$. Keywords: Sublinear elliptic problem, weight function, nonnegative solution, positive solution, minimax method, mountain pass, multiplicity. MSC: 35J20, 35J25. [ Fulltext-pdf  (119  KB)] for subscribers only.