Liouville type theorems for positive stable solutions of double phase problems with negative exponent

Belgacem Rahal; Abderraouf Ghallabi

doi:10.4171/zaa/1833

JournalszaaOnline First

Liouville type theorems for positive stable solutions of double phase problems with negative exponent

Belgacem Rahal
University of Kairouan, Tunisia; University of Monastir, Tunisia
Abderraouf Ghallabi
University of Kairouan, Tunisia

A subscription is required to access this article.

Abstract

In this paper, we study positive stable weak solutions to the double phase problem

{div (w (x) ∣\nabla u ∣^{p - 2} \nabla u + ∣\nabla u ∣^{r - 2} \nabla u) = f (x) u^{- q} (w (x) ∣\nabla u ∣^{p - 2} + ∣\nabla u ∣^{r - 2}) \frac{\partial u}{\partial η} = - u^{- θ} in R_{+}^{N}, on \partial R_{+}^{N},

where $p \geq r \geq 2$ , $θ, q > 0$ , $a < b + p$ , and $w, f \in L_{loc}^{1} (R_{+}^{N})$ are nonnegative functions such that $w (x) \leq C_{1} ∣ x ∣^{a}$ and $f (x) \geq C_{2} ∣ x ∣^{b}$ for large $∣ x ∣$ , where $C_{1}, C_{2} > 0$ . Under some appropriate assumptions on $p$ , $q$ , $r$ , $θ$ , $a$ , $b$ , and $N$ , we prove the non-existence of positive stable weak solutions.

Cite this article

Belgacem Rahal, Abderraouf Ghallabi, Liouville type theorems for positive stable solutions of double phase problems with negative exponent. Z. Anal. Anwend. (2026), published online first

DOI 10.4171/ZAA/1833