Nodal Solutions for a Quasilinear Elliptic Equation Involving the p-Laplacian and Critical Exponents

This paper is concerned with the following type of quasilinear elliptic equations in R-N involving the p-Laplacian and critical growth: -Delta(p)u + V(vertical bar x vertical bar)vertical bar u vertical bar(p-2)u - Delta(p)(vertical bar u vertical bar(2))u = lambda vertical bar u vertical bar(q-2)u + vertical bar u vertical bar(2p)*(-2)u, which arises as a model in mathematical physics, where 2 < p < N, p* = Np/N-p. For any given integer k >= 0, by using change of variables and minimization arguments, we obtain, under some additional assumptions on p and q, a radial sign- changing nodal solution with k + 1 nodal domains. Since the critical exponent appears and the lower order term ( obtained by a transformation) may change sign, we shall use delicate arguments.