Abstract
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.
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