Abstract

We consider the problem (Formula presented.) (Formula presented.) where Ω is a bounded smooth domain in (Formula presented.), (Formula presented.), that exhibits certain symmetries and contains the origin, (Formula presented.), (Formula presented.), (Formula presented.), and (Formula presented.) is a small parameter. By using the Lyapunov–Schmidt reduction method and topological degree theory, for each sufficiently large (Formula presented.), we construct sign-changing solutions to (Formula presented.) exhibiting k negative spikes at the vertices of a regular polygon and a single positive spike at the origin.