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arXiv · 1805.11870

Positive multipeak solutions to a zero mass problem in exterior domains

Mónica Clapp·Liliane A. Maia·Benedetta Pellacci
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Abstract

We establish the existence of positive multipeak solutions to the nonlinear scalar field equation with zero mass $$-\Delta u = f(u), \qquad u\in D_0^{1,2}(\Omega_R),$$ where $\Omega_R:=\{x \in \mathbb{R}^N:|u|>R\}$ with $R>0$, $N\geq4$, and the nonlinearity $f$ is subcritical at infinity and supercritical near the origin. We show that the number of positive multipeak solutions becomes arbitrarily large as $R \to \infty$.

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Mónica Clapp, Liliane A. Maia, Benedetta Pellacci. 2018-05-30. Positive multipeak solutions to a zero mass problem in exterior domains. https://doi.org/10.1142/s0219199719500627

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