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. Electronic Journal of Differential Equations, 2017(208), pp. 1-14.
Rights
Attribution 4.0 International