Infinitely many solutions for a class of quasilinear Schrödinger equations involving sign-changing weight functions

ABSTRACT

Using a change of variables and the constrained critical point theory, we first prove the existence and multiplicity of solutions for a class of quasilinear Schrödinger equations. Next, we consider a quasilinear equation related to the superfluid film in plasma physics with a sign-changing weight function. Using a new natural constraint, we establish the existence of infinitely many solutions for the equation.

KEYWORDS:

• Quasilinear Schrödinger equation
• infinitely many solutions
• sign-changing weight function

AMS SUBJECT CLASSIFICATIONS:

• 35J10
• 35J20
• 35J62

Acknowledgements

The author would like to thank Prof. Andrzej Szulkin for his valuable comments and suggestions.

Notes

No potential conflict of interest was reported by the author.