Ground state solutions for fractional p-Kirchhoff equation

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. <i>Electronic Journal of Differential Equations, 2022</i>(61), pp. 1-14.

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Attribution 4.0 International

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