Electron. J. Differential Equations, Vol. 2017 (2017), No. 230, pp. 1-17.

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

Sihua Liang, Vicentiu D. Radulescu

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.

Submitted July 10, 2017. Published September 22, 2017.
Math Subject Classifications: 35R11, 35A15, 47G20.
Key Words: Kirchhoff-type problems; Schrodinger-Choquard equations; fractional p-Laplacian; critical exponent; variational methods.

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Sihua Liang
College of Mathematics
Changchun Normal University
Changchun 130032, Jilin, China
email: liangsihua@126.com
Vicentiu D. Radulescu
Department of Mathematics, Faculty of Sciences
King Abdulaziz University, P.O. Box 80203
Jeddah 21589, Saudi Arabia
email: vicentiu.radulescu@imar.ro

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