We study the resonant quasilinear problem $-\Delta_p u = \lambda_p u^{p-1} + \lambda g(u) in \Omega, u \ge 0 in \Omega, u_{\partial\Omega} = 0,$ where $\Omega\subset\mathbb{R}^n$ is a smooth, bounded domain, $λ_p$ is the first eigenvalue of $-\Delta_p$ in $\Omega$, and $g : [0, +\infty)\to\mathbb{R}$ is a continuous and subcritical term. By means of variational arguments, we prove the existence of non-negative solutions for any $\lambda > 0$; positive solutions for sufficiently small $\lambda > 0$. Our results generalize the ones recently obtained by different techniques in the case $p = 2$.

Non-negative solutions and strong maximum principle for a resonant quasilinear problem

Anello, Giovanni
Primo
;
Cammaroto, Filippo
Secondo
;
Vilasi, Luca
Ultimo
2023-01-01

Abstract

We study the resonant quasilinear problem $-\Delta_p u = \lambda_p u^{p-1} + \lambda g(u) in \Omega, u \ge 0 in \Omega, u_{\partial\Omega} = 0,$ where $\Omega\subset\mathbb{R}^n$ is a smooth, bounded domain, $λ_p$ is the first eigenvalue of $-\Delta_p$ in $\Omega$, and $g : [0, +\infty)\to\mathbb{R}$ is a continuous and subcritical term. By means of variational arguments, we prove the existence of non-negative solutions for any $\lambda > 0$; positive solutions for sufficiently small $\lambda > 0$. Our results generalize the ones recently obtained by different techniques in the case $p = 2$.
2023
File in questo prodotto:
File Dimensione Formato  
Non-negative solutions and strong maximum principle.pdf

solo gestori archivio

Tipologia: Versione Editoriale (PDF)
Licenza: Copyright dell'editore
Dimensione 296.47 kB
Formato Adobe PDF
296.47 kB Adobe PDF   Visualizza/Apri   Richiedi una copia
Pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11570/3282548
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 0
  • ???jsp.display-item.citation.isi??? 0
social impact