Existence of infinitely many solutions for degenerate Kirchhoff-type Schrodinger-Choquard equations

Abstract

In this article we study a class of Kirchhoff-type Schrodinger-Choquard equations involving the fractional p-Laplacian. By means of Kajikiya's new version of the symmetric mountain pass lemma, we obtain the existence of infinitely many solutions which tend to zero under a suitable value of $\lambda$. The main feature and difficulty of our equations arise in the fact that the Kirchhoff term M could vanish at zero, that is, the problem is degenerate. To our best knowledge, our result is new even in the framework of Schrodinger-Choquard problems.

Keywords

• Kirchhoff-type problems
• Schrodinger-Choquard equations
• fractional p-Laplacian
• critical exponent
• variational methods