Chen, SitongTang, Xianhua2022-02-222022-02-222018-08-29Chen, S., & Tang, X. (2018). Existence of ground state solutions for quasilinear Schrödinger equations with variable potentials and almost necessary nonlinearities. <i>Electronic Journal of Differential Equations, 2018</i>(157), pp. 1-13.1072-6691https://hdl.handle.net/10877/15406In this article we prove the existence of ground state solutions for the quasilinear Schrödinger equation -∆u + V(x)u - ∆(u2)u = g(u), x ∈ ℝN, 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.Text13 pages1 file (.pdf)enAttribution 4.0 InternationalQuasilinear Schrödinger equationGround state solutionBerestycki-Lions conditionsArticle