Electronic Journal of Differential Equations, Vol. 2025 (2025), No. 47, pp. 1-13.

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

Authors: Sigifredo Herron (Univ. Nacional de Colombia, Medellin, Colombia)
         Emer Lopera (Univ. Nacional de Colombia, Manizales, Colombia)
         Diana Sanchez (Univ. Nacional de Colombia, Manizales, Colombia)

Abstract:
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. 

Submitted March 2, 2025. Published May 08, 2025.
Math Subject Classifications: 35B09, 35B50, 35B51, 35D30, 35G30, 35J10, 35J92, 47H10.
Key Words: Subsolution; supersolution; multiple solutions; p-Laplacian; Schrodinger type operator