Multiple solutions for a quasilinear Schrodinger equation involving critical Hardy-Sobolev exponent with Robin boundary condition

In this paper, we consider the existence of multiple solutions for a quasilinear Schrodinger equation with Robin boundary condition involving critical Hardy-Sobolev exponent as follows: {-Delta u - Delta(u(2))u + u = (u(2))(2+)((s)-1)/vertical bar x vertical bar(s)u + f (x, u) in Omega, partial derivative u/partial derivative n + beta(X)u = 0 on partial derivative Omega, where f is an element of C((Omega) over bar x R, R) satisfies suitable condition. Using variable substitution and Mountain Pass Theorem, we prove that the above equation admits at least two nontrivial solutions.