Quasilinear Schr?dinger Equations with Asymptotically Linear Nonlinearities *

摘要

We deal with the existence of nonzero solution for the quasilinear Schr?dinger equation -△u + V(x)u - △(u~2)u = g(x, u), x∈ R~N,u∈ H~1(R~N), where V is a positive potential and the nonlinearity g(x, s) behaves like K_0(x)s at the origin and like K_∞(x)|s|~p, 1 ≤ p ≤ 3, at infinity. In the proofs we apply minimization methods.