MULTIPLICITY AND CONCENTRATION BEHAVIOUR OF POSITIVE SOLUTIONS FOR SCHRODINGER-KIRCHHOFF TYPE EQUATIONS INVOLVING THE p-LAPLACIAN IN RN

In this article, we study the multiplicity and concentration behavior of positive solutions for the p-Laplacian equation of Schrodinger-Kirchhoff type -epsilon M-p(epsilon(p-N)integral(RN)vertical bar del u vertical bar(p))Delta(p)u + V(x)vertical bar u vertical bar(p-2)u = f(u) in R-N, where Delta(p) is the p-Laplacian operator, 1 < p < N, M : R+ -> R+ and V : R-N -> R+ are continuous functions, epsilon is a positive parameter, and f is a continuous function with subcritical growth. We assume that. V satisfies the local condition introduced by M. del Pino and P. Felmer. By the variational methods, penalization techniques, and LyusternikSchnirelrnann theory, we prove the existence, multiplicity-, arid concentration of solutions for the above equation.