Multi-bump solutions for logarithmic Schrödinger equations

Multi - Bump Solutions on Lattices

We consider the following semi-linear elliptic equation with critical exponent: −∆u = K(x)u n+2 n−2 , u > 0 in R, where n ≥ 3, K > 0 is periodic in (x1, ..., xk) with 1 ≤ k < n−2 2 . Under some natural conditions on K near a critical point, we prove the existence of multi-bump solutions where the centers of bumps can be placed in some lattices in R, including infinite lattices. We also show tha...

Soliton Solutions for Quasilinear Schrödinger Equations

Existence of infinitely many solutions for coupled system of Schrödinger-Maxwell's equations

Existence and Symmetry of Multi-bump Solutions for Nonlinear Schrr Odinger Equations

We study the existence and symmetry property of multi-bump solutions of Especially when the potential V is radially symmetric, multi-bump solutions are constructed with bumps concentrating on a single connected component of the set of global minimum points of V. Furthermore, conditions are given to assure that the multi-bump solutions obtained have prescribed subgroups of O(N) as their exact sy...

Sign-changing Multi-bump Solutions for Nonlinear Schrödinger Equations with Steep Potential Wells

We study the nonlinear Schrödinger equations: (Pλ) −∆u+(λa(x)+1)u = |u|p−1u, u ∈ H(R ), where p > 1 is a subcritical exponent, a(x) is a continuous function satisfying a(x) ≥ 0, 0 < lim inf |x|→∞ a(x) ≤ lim sup|x|→∞ a(x) < ∞ and a−1(0) consists of 2 connected bounded smooth components Ω1 and Ω2. We study the existence of solutions (uλ) of (Pλ) which converge to 0 in RN \ (Ω1 ∪Ω2) and to a presc...