Existence of ground state solution for semilinear -Laplace equation

ABSTRACT

This paper explores the existence of ground state solutions for a class of semilinear ${\mathrm{\Delta }}_{\alpha }$-Laplace equations $-{\mathrm{\Delta }}_{\alpha }u+V(x)u=f(x,u),x\in {\mathbb{R}}^N,$ where $V\in C({\mathbb{R}}^N,\mathbb{R})$ is a coercive potential, ${\mathrm{\Delta }}_{\alpha }$ is a strongly degenerate elliptic operator, f is a function with more general superlinear conditions or asymptomatic linear conditions.

KEYWORDS:

• Strongly degenerate elliptic operator
• coercive potential
• ground state solution

AMS SUBJECT CLASSIFICATIONS:

• 35J60
• 35J25
• 35B33
• 35J70

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by Chongqing Municipal Education Commission [grant number KJQN20190081] Chongqing Technology and Business University [grant number CTBUZDPTTD201909] National Natural Science Foundation of China [grant number 11861046].