Ground state solutions for fractional p-Kirchhoff equation
Files
Date
2022-08-19
Authors
Wang, Lixiong
Chen, Haibo
Yang, Liu
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
We study the fractional p-Kirchhoff equation
(α + b ∫ℝN ∫ℝ |u(x)-u(y)|p/|x-y|N+ps dx dy (-∆)s p u - μ|u|p-2u = |u|q-2u, x ∈ ℝN, where (-∆)s p is the fractional p-Laplacian operator, a and b are strictly positive real numbers, s ∈ (0, 1), 1 < p < N/s, and p < q < p*s - 2 with p*s = Np/N-ps. By using the variational method, we prove the existence and uniqueness of global minimum or mountain pass type critical points on the Lp-normalized manifold S(c) ≔ {u ∈ Ws,p(ℝN) : ∫ℝN |u|pdx = cp}.
Description
Keywords
Variational method, L^p-normalized critical point, Fractional, p-Kirchhoff equation, Uniqueness
Citation
Wang, L., Chen, H., & Yang, L. (2022). Ground state solutions for fractional p-Kirchhoff equation. Electronic Journal of Differential Equations, 2022(61), pp. 1-14.
Rights
Attribution 4.0 International