On a Schrödinger equation with periodic potential involving critical growth
نویسندگان
چکیده
The main purpose of this paper is to establish the existence of a solution of the semilinear Schrödinger equation −∆u + V (x)u = f(u), in R where V is a 1-periodic functions with respect to x, 0 lies in a gap of the spectrum of −∆ + V , and f(s) behaves like ± exp(αs) when s → ±∞.
منابع مشابه
On a class of periodic quasilinear Schrödinger equations involving critical growth in R
We consider the equation −∆u + V (x)u − k(∆(|u|2))u = g(x, u), u > 0, x ∈ R, where V : R → R and g : R × R → R are two continuous 1−periodic functions. Also, we assume g behaves like exp(β|u|4) as |u| → ∞. We prove the existence of at least one weak solution u ∈ H(R) with u ∈ H(R). Mountain pass in a suitable Orlicz space together with MoserTrudinger are employed to establish this result. Such ...
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