In this paper,we study the following generalized quasilinear Schrdinger equations with critical or supercritical growths-div(g^2(u)▽u) + g(u)g′(u)|▽u|~2+ V(x)u = f(x,u) + λ|u|^(p-2)u,x∈R^N,where λ>0,N≥3,g...In this paper,we study the following generalized quasilinear Schrdinger equations with critical or supercritical growths-div(g^2(u)▽u) + g(u)g′(u)|▽u|~2+ V(x)u = f(x,u) + λ|u|^(p-2)u,x∈R^N,where λ>0,N≥3,g:R → R^+ is a C^1 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 Schrdinger equations with critical or supercritical growths-div(g^2(u)▽u) + g(u)g′(u)|▽u|~2+ V(x)u = f(x,u) + λ|u|^(p-2)u,x∈R^N,where λ>0,N≥3,g:R → R^+ is a C^1 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.
