Zhenluo Lou, Xiaoyao Jia, The existence of radial positive solutions of a class of quasi-linear elliptic equations, Vol. 2025 (2025), No. 24, pp. 1-9

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DOI: 10.23952/jnfa.2025.24

Received March 1, 2025; Accepted July 28, 2025; Published September 2, 2025

Abstract. In this paper, we study the weighted embedding theorem in Orlicz-Sobolev spaces, and we obtain the existence of nontrivial solution of the following equation
$-\Delta_{\Phi} u = |x|^{\alpha} |u|^{q-2}u,$ in $B,$
$u= 0$ on $\partial B,$
where $B \subset \mathbb R^N~(N \geq 3)$ is the unique ball, $\alpha >0$ is a constant, $\phi \in C^1(0,+\infty)$ and $2 <q < \infty$ . If the nonlinear term is sub-linear, by Clark's theorem, we obtain the existence of infinity many solutions of the equation.

How to Cite this Article:
Z. Lou, X. Jia, The existence of radial positive solutions of a class of quasi-linear elliptic equations, J. Nonlinear Funct. Anal. 2025 (2025) 24.