From the authors’ introduction: The present paper is concerned with the singularly perturbed elliptic problem:
where is a bounded smooth domain in , is a constant, for and for , and denotes the normal derivative at . This is known as the stationary equation of the Keller-Segel system in chemotaxis. It can also be seen as the limiting stationary equation of the so-called Gierer-Meinhardt system in biological pattern formation.
In this paper, we obtain a multiplicity result of interior peak solutions by using a category theory. Actually, we also able to handle more general nonlinearities than the power . (Given two closed sets , we say the category of is , denoted by , where is the smallest number such that may be covered by closed contractible sets in . We call the category of the strictly positive integer ).