EXISTENCE OF GROUND STATE SOLUTIONS FOR QUASILINEAR SCHRÖDINGER EQUATIONS WITH VARIABLE POTENTIALS AND ALMOST NECESSARY NONLINEARITIES
EXISTENCE OF GROUND STATE SOLUTIONS FOR QUASILINEAR SCHRÖDINGER EQUATIONS WITH VARIABLE POTENTIALS AND ALMOST NECESSARY NONLINEARITIES
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发表时间：
2018
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通讯作者：
Sitong Chen;Xianhua Tang;Binlin Zhang
中科院分区：
文献类型：
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作者：
Sitong Chen;Xianhua Tang;Binlin Zhang
本文证明了拟线性薛定谔方程−∆u+V(X)u−∆(U)u=g(U)，x∈R的基态解的存在性，其中N≥3，V∈C1(RN，[0，∞))满足弱衰变条件，g∈C(R，R)满足几乎必要的Berestycki-Lions条件。特别地，我们引入了一些新的不等式和技巧来克服紧性的不足。
In this article we prove the existence of ground state solutions for the quasilinear Schrödinger equation −∆u + V (x)u−∆(u)u = g(u), x ∈ R , where N ≥ 3, V ∈ C1(RN , [0,∞)) satisfies mild decay conditions and g ∈ C(R, R) satisfies Berestycki-Lions conditions which are almost necessary. In particular, we introduce some new inequalities and techniques to overcome the lack of compactness.