【摘 要】
：
In this talk we consider singularly perturbed nonlinear Schr(o)dinger equations {-ε2△u + V (x)u = f(u) in RN, u > 0 in RN,(*) u ∈H1(RN),where N≥3, V 2 C
【机 构】
：
WasedaUniversity,Japan
【出 处】
：
2016年非线性偏微分方程和变分方法及其应用研讨会(Workshop on Nonlinear PDEs and Cal
论文部分内容阅读
In this talk we consider singularly perturbed nonlinear Schr(o)dinger equations {-ε2△u + V (x)u = f(u) in RN, u > 0 in RN,(*) u ∈H1(RN),where N≥3, V 2 C(RN;R) and f is a nonlinear term which satisfies the so-called Berestycki- Lions conditions. We assume that there exists a bounded domain Ω(()RN such that m0≡infx∈Ω V(x) < infx∈(e)Ω x2@ V(x) and we set K = {x∈Ω ; V (x) = m0}. For ε> 0 small we prove the existence of at least cupl(K) + 1 solutions to concentrating, as ε→ 0 around K. We remark that, under our assumptions of f, the search of solutions to (*) cannot be reduced to the study of the critical points of a functional restricted to a Nehari manifold. If time allows, we also deal with nonlinear Schr(o)dinger equations with a magnetic field. This talk is based on joint works with S. Cingolani and L. Jeanjean.
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