Infinite many blow-up solutions for a Schrödinger quasilinear elliptic problem with a non-square diffusion term

Abstract

In this paper, we consider existence of positive solutions for the quasilinear elliptic Schrödinger problem

where and are non-negative and continuous functions with g being non-decreasing as well, , and . By a dual approach we establish sufficient conditions for existence and multiplicity of solutions for this problem.

Keywords:

• Schrödinger equations
• Blow up solutions
• Quasilinear problems
• Non-square diffusion
• Multiplicity of solutions

AMS Subject Classifications:

• 35J10
• 35J92
• 35B07
• 35B08
• 35B44

Acknowledgements

This paper was completed while the first author was visiting Professor Haim Brezis at Rutgers University. He thanks Professor Brezis for his incentive and hospitality. At this time, the second author was visiting Professor Zhitao Zhang at Chinese Academy of Sciences. He is grateful for his invitation and hospitality as well.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the CAPES/Brazil [Proc. number 2788/2015-02]; CNPq/Brazil [Proc. number [232373/2014-0].