RADIALLY SYMMETRIC SOLUTIONS FOR QUASILINEAR ELLIPTIC EQUATIONS INVOLVING NONHOMOGENEOUS OPERATORS IN AN ORLICZ-SOBOLEV SPACE SETTING

We investigate the following elliptic equations: {-M(integral(RN)phi(vertical bar del u vertical bar(2))dx)div(phi '(vertical bar del u vertical bar(2))del u)+vertical bar u vertical bar(alpha-2)u = lambda h(x,u), in R-N, u(x) -> 0, as vertical bar u vertical bar -> infinity, in where N >= 2, 1 < p < q < N, alpha < q, 1 < alpha < p*q'/p' with p* = Np/N-p, phi(t) behaves like t(q/2) for smalltand t(p/2) for larget, andp ' andq ' are the conjugate exponents ofpandq, respectively. We study the existence of nontrivial radially symmetric solutions for the problem above by applying the mountain pass theorem and the fountain theorem. Moreover, taking into account the dual fountain theorem, we show that the problem admits a sequence of small-energy, radially symmetric solutions.