Existence of three positive solutions for a p-sublinear problem involving a Schrodinger p-Laplacian type operator - Sigifredo Herron; Emer Lopera; Diana Sanchez (Electronic Journal of Differential Equations)
We prove the existence of three positive solutions for the problem $$\disolaylines{ -\Delta_p u + V (x)\varphi_p(u)=\lambda f(u),\quad x\in \Omega, \cr u(x)=0, \quad x\in \partial\Omega, } $$ where $\lambda >0$, $\Delta_p$ is the $p$-Laplacian operator, $N>p>1$, $\varphi_p (s):=|s|^{p-2}s$, $s\in \mathbb{R}$, $\Omega$ is a bounded domain in $\mathbb{R}^N$ with connected and smooth boundary. In our study, $ V \in L^\infty (\Omega)$ and $f:[0,\infty)\to \mathbb{R}$ is a $C^1$ function. The reaction term, $f$, is increasing and $p$-sublinear at infinity. Our method relies on sub-super solution techniques and the use of a theorem on the existence of multiple fixed points. We extend some results known in the literature.