Existence of ground states for fractional Kirchhoff equations with general potentials via Nehari-Pohozaev manifold
Files
Date
2018-07-13
Authors
Chen, Jing
Tang, Xianhua
Chen, Sitong
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
We consider the nonlinear fractional Kirchhoff equation
(α + b ∫ℝ3 |(-∆)α/2u|2 dx) (-∆)αu + V(x)u = ƒ(u) in ℝ3, u ∈ Hα (ℝ3),
where α > 0, b ≥ 0, α ∈ (3/4, 1) are three constants, V(x) is differentiable and ƒ ∈ C1 (ℝ, ℝ). Our main results show the existence of ground state solutions of Nehari-Pohozaev type, and the existence of the least energy solutions to the above problem with general superlinear and subcritical nonlinearity. These results are proved by applying variational methods and some techniques from [27].
Description
Keywords
Fractional Kirchhoff equation, Nehari-Pohozaev manifold, Ground state solutions
Citation
Chen, J., Tang, X., & Chen, S. (2018). Existence of ground states for fractional Kirchhoff equations with general potentials via Nehari-Pohozaev manifold. <i>Electronic Journal of Differential Equations, 2018</i>(142), pp. 1-21.
Rights
Attribution 4.0 International