In this paper, we study the following generalized quasilinear Schrodinger equa- tions with critical or supercritical growths-div（g2（u）△u） ＋ g（u）g＇（u）｜△u｜2 ＋ V（x）u = f（x, u） ＋ λ｜u｜P-2 u, x ∈ RN,...In this paper, we study the following generalized quasilinear Schrodinger equa- tions with critical or supercritical growths-div（g2（u）△u） ＋ g（u）g＇（u）｜△u｜2 ＋ V（x）u = f（x, u） ＋ λ｜u｜P-2 u, 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, lim ｜s｜→＋ ∞g（s）/｜s｜α-1：= β 〉 0 for some α≥ 1 and （α- 1）g（s） 〉 g＇（s）s for all s 〉 0 and p≥α2＊.Under some suitable conditions, we prove that the equation has a nontrivial solution for smallλ 〉 0 using a change of variables and variational method.展开更多
基金supported in part by the National Natural Science Foundation of China(1150140311461023)the Shanxi Province Science Foundation for Youths under grant 2013021001-3
文摘In this paper, we study the following generalized quasilinear Schrodinger equa- tions with critical or supercritical growths-div（g2（u）△u） ＋ g（u）g＇（u）｜△u｜2 ＋ V（x）u = f（x, u） ＋ λ｜u｜P-2 u, 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, lim ｜s｜→＋ ∞g（s）/｜s｜α-1：= β 〉 0 for some α≥ 1 and （α- 1）g（s） 〉 g＇（s）s for all s 〉 0 and p≥α2＊.Under some suitable conditions, we prove that the equation has a nontrivial solution for smallλ 〉 0 using a change of variables and variational method.
