Ground solutions for critical quasilinear elliptic equations via Pohožaev manifold method

Abstract

The paper deals with the following problem:

where is a parameter, and , . Under some certain assumptions on V(x), we establish the existence of ground-state solutions for quasi-linear elliptic equations with Sobolev exponent via the method of Pohožaev manifold, the monotonic trick and global compactness lemma. Some recent results are extended.

Keywords:

• Quasi-linear elliptic equations
• ground-state solutions
• concentration–compactness principle
• Pohožaev manifold

AMS Subject Classifications:

• 35J20
• 35J65
• 35J60

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by National Natural Science Foundation of China [11671403], [11671236]; Key Basic Research for Higher Education of Henan Province [17A110019].