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 $$\disolaylines{ -\Delta_p u + V (x)\varphi_p(u)=\lambda f(u),\quad x\in \Omega, \cr u(x)=0, \quad x\in \partial\Omega, } $$ where $\lambda >0$, $\Delta_p$ is the $p$-Laplacian operator, $N>p>1$, $\varphi_p (s):=|s|^{p-2...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2025-05-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2025/47/abstr.html |
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| Summary: | 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. |
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| ISSN: | 1072-6691 |