Abstract
We are concerned with the following equation: $$ -\varepsilon^2\Delta u+V(x)u=f(u),\quad u(x)> 0\quad \mbox{in } \mathbb{R}^2. $$ By a variational approach, we construct a solution $u_\varepsilon$ which concentrates, as $\varepsilon \to 0$, 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.
Citation
Daniele Cassani. João Marcos do Ó. Jianjun Zhang. "Multi-bump solutions for singularly perturbed Schrödinger equations in $\mathbb{R}^2$ with general nonlinearities." Topol. Methods Nonlinear Anal. 49 (1) 205 - 231, 2017. https://doi.org/10.12775/TMNA.2016.074
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