We are concerned with the following equation: −ε2 ∆u + V (x)u = f(u), u(x) > 0 in ℝ2. By a variational approach, we construct a solution uε which concentrates, as ε → 0, around arbitrarily given isolated local minima of the confining potential V: here the nonlinearity f has a quite general Moser’s critical growth, as in particular we do not require the monotonicity of f(s)/s nor the Ambrosetti–Rabinowitz condition.

Multi-bump solutions for singularly perturbed Schrödinger equations in ℝ2 with general nonlinearities

CASSANI, DANIELE;ZHANG, JIANJUN
2017

Abstract

We are concerned with the following equation: −ε2 ∆u + V (x)u = f(u), u(x) > 0 in ℝ2. By a variational approach, we construct a solution uε which concentrates, as ε → 0, around arbitrarily given isolated local minima of the confining potential V: here the nonlinearity f has a quite general Moser’s critical growth, as in particular we do not require the monotonicity of f(s)/s nor the Ambrosetti–Rabinowitz condition.
Critical growth; Schrödinger equations; Semiclassical states
Cassani, Daniele; Do Ó, João Marcos; Zhang, Jianjun
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11383/2054516
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