Multiple solutions for a class of Kirchhoff-type equation with critical growth

In this paper, we study the multiplicity of solutions to a class of Kirchhoff- type equation with critical growth - ( a + b integral(3)(R) |del u|(2)dx ) Delta u + V(x)u = lambda h(x) f (u) + g(x)u(5) in R-3, where a, b > 0, lambda is a positive parameter and f is a continuous nonlinearity with subcritical growth. Under suitable conditions on the potentials V(x), h(x) and g(x), we prove the multiplicity results and investigate the relation between the number of solutions with the topology of the set where g attains its maximum value for small values of the parameter lambda. The proofs are based on Nehari manifold and Lusternik-Schnirelmann theory.