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

where Ω is a smooth bounded domain in ${\mathbb{R}}^N$, $N⩾3$, $2^{⁎}=\frac{2N}{N-2}$ and $\epsilon >0$ is a small parameter. In particular we prove that if Ω is convex and satisfies a certain symmetry, then a nodal four-bubble solution exists with two positive and two negative bubbles.