Multi-bubble nodal solutions for slightly subcritical elliptic problems in domains with symmetries

Abstract

We study the existence of sign-changing solutions with multiple bubbles to the slightly subcritical problem $$-Δu=|u|^{2^*-2-\e}u \hbox{in}Ω, \quad u=0 \hbox{on}\partial Ω,$$ where $\Omega$ is a smooth bounded domain in ${\mathbb{R}}^N$, $N\ge 3$, $2^{\ast }=\frac{2N}{N-2}$ and $\e>0$ is a small parameter. In particular we prove that if $\Omega$ is convex and satisfies a certain symmetry, then a nodal four-bubble solution exists with two positive and two negative bubbles.

References in corpus (1)

• Conformal approach to cylindrical DLA

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