Nodal solutions to (p, q)-Laplacian equations with critical growth

In this paper, a class of (p, q)-Laplacian equations with critical growth is taken into consideration: { -Delta(p)u - Delta(q)u + (vertical bar u vertical bar(p-2) + vertical bar u vertical bar(q-2))u + lambda phi vertical bar u vertical bar(q-2)u = mu g(u) + vertical bar u vertical bar(q*-2)u, x is an element of R-3, -Delta phi = vertical bar u vertical bar(q), x is an element of R-3, where Delta(xi)u = div(vertical bar del u vertical bar(xi-2) del u) is the xi-Laplacian operator (xi = p, q), 3/2 < p < q < 3, lambda and mu are positive parameters, q* = 3q/(3 - q) is the Sobolev critical exponent. We use a primary technique of constrained minimization to determine the existence, energy estimate and convergence property of nodal (that is, sign-changing) solutions under appropriate conditions on g, and thus generalize the existing results.