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This paper is concerned with the existence and qualitative property of solutions for a Hénon-like equationwhere Ω = {x ∈ ℝN : 1 < |x| < 3} with N ≥ 4, 2* = 2N/(N − 2), τ > 0 and ε > 0 is a small parameter. For any given k ∈ ℤ+, we construct positive solutions concentrating simultaneously at 2k different points for ε sufficiently small, among which k points are near the interior boundary {x ∈ ℝN : |x| = 1} and the other k points are near the outward boundary {x ∈ ℝN : |x| = 3}. Moreover, the 2k points tend to the boundary of Ω as ε goes to 0. [ABSTRACT FROM PUBLISHER]

In this paper, we are concerned with the existence of multi-bump solutions for a nonlinear Schrödinger equations with electromagnetic fields. We prove under some suitable conditions that for any positive integer m, there exists ε(m) > 0 such that, for 0 < ε < ε(m), the problem has an m-bump complex-valued solution. As a result, when ε → 0, the equation has more and more multi-bump complex-valued solutions. [ABSTRACT FROM PUBLISHER]