Existence of three positive solutions for a p-sublinear problem involving a Schrodinger p-Laplacian type operator

We prove the existence of three positive solutions for the problem $$\displaylines{ -\Delta_p u + V (x)\varphi_p(u)=\lambda f(u),\quad x\in \Omega, \cr u(x)=0, \quad x\in \partial\Omega, } $$ 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. For more information see https://ejde.math.txstate.edu/Volumes/2025/47/abstr.html