ABSTRACT
In this paper, we study the following semilinear Kirchhoff type equation: where is a parameter, a, b are positive constants, V and f are continuous functions. Under certain assumptions on V and f, we investigate the relation between the number of solutions and the topology of the set where V attains its local minimum for small ε. We also describe the concentration phenomena of solutions as . The proof is based on the method of Nehari manifold, penalization techniques and Ljusternik–Schnirelmann category theory.
Disclosure statement
No potential conflict of interest was reported by the authors.