Existence of Ground States for Kirchhoff-Type Problems with General Potentials
The Journal of Geometric Analysis(2020)
摘要
In this paper, we consider the following Kirchhoff-type problem: {[ -( a+b∫ _ℝ^3|∇ u|^2dx) u+V(x)u=f(u), x∈ℝ^3;; u∈ H^1(ℝ^3), ]. where a, b> 0 , V∈𝒞(ℝ^3, ℝ) and f∈𝒞(ℝ, ℝ) . Using variational method and some new analytical techniques, we show the existence of ground state solutions for the above problem. Assumptions imposed on the potential V and the nonlinearity f are general, and they are satisfied by several functions. Our results generalize and improve the ones obtained recently in [Li and Ye, J. Differential Equations (2014)], [Tang and Chen, Calc. Var. Partial Differential Equations (2017)], [Guo, J. Differential Equations (2015)] and some other related literature.
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关键词
Kirchhoff-type problem, Ground states, General potentials, Variational method, 35J20, 35J65
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