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
2017-01-01
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.
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