Existence of infinitely many solutions for fractional p-Laplacian equations with sign-changing potential

Date

2017-09-08

Authors

Zhang, Youpei
Tang, Xianhua
Zhang, Jian

Journal Title

Journal ISSN

Volume Title

Publisher

Texas State University, Department of Mathematics

Abstract

In this article, we prove the existence of infinitely many solutions for the fractional p-Laplacian equation (-∆)spu + V(x)|u|p-2 u = ƒ(x, u), x ∈ ℝN where s ∈ (0, 1), 2 ≤ p < ∞. Based on a direct sum decomposition of a space Es, we investigate the multiplicity of solutions for the fractional p-Laplacian equation in ℝN. The potential V is allowed to be sign-changing, and the primitive of the nonlinearity ƒ is of super-p growth near infinity in u and allowed to be sign-changing. Our assumptions are suitable and different from those studied previously.

Description

Keywords

Fractional p-Laplacian, Multiple solutions, Variational methods, Sign-changing potential

Citation

Zhang, Y., Tang, X., & Zhang, J. (2017). Existence of infinitely many solutions for fractional p-Laplacian equations with sign-changing potential. <i>Electronic Journal of Differential Equations, 2017</i>(208), pp. 1-14.

Rights

Attribution 4.0 International

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