Resumen de Ground State Solutions for Generalized Quasilinear Schrödinger Equations with Critical Growth

Quanqing Li, Jian Zhang, Jianjun Nie

• In this paper, we study the following generalized quasilinear Schrödinger equation with critical growth −div(g2(u)∇u) + g(u)g (u)|∇u| 2 + V(x)u = λ f (x, u) + |u| α2∗−2u, x ∈ RN , where λ > 0, N ≥ 3, g : R → R+ is a C1 even function, g(0) = 1, g (s) ≥ 0 for all s ≥ 0, g(s) = β|s| α−1 + O(|s| γ −1) as s → ∞ for some constants α ∈ [1, 2],β> 0, γ <α and (α − 1)g(s) ≥ g (s)s for all s ≥ 0. Under some suitable conditions on the potential and nonlinearity, we obtain the existence of ground state solutions for large λ by using dual approach and Nehari manifold method.