Existence of radial bounded solutions for some quasilinear elliptic equations in RN

We study the quasilinear equation (P) -div(A(x, u)vertical bar del u vertical bar(p-2)del u) + 1/p A(t)(x, u)vertical bar del u vertical bar(p)+vertical bar u vertical bar(p-2)u = g(x, u) in R-N, with N >= 3, p > 1, where A(x, t), A(t)(x, t) = partial derivative A/partial derivative t (x, t) and g(x, t) are Caratheodory functions on R-N x R. Suitable assumptions on A(x, t) and g(x, t) set off the variational structure of (P) and its related functional J is C-1 on the Banach space X = W-1,W-p(R-N) boolean AND L-infinity(R-N). In order to overcome the lack of compactness, we assume that the problem has radial symmetry, then we look for critical points of J restricted to X-r, subspace of the radial functions in X. Following an approach which exploits the interaction between parallel to . parallel to(X) and the norm on W-1,W-p(R-N), we prove the existence of at least one weak bounded radial solution of (P) by applying a generalized version of the Ambrosetti-Rabinowitz Mountain Pass Theorem. (C) 2019 Elsevier Ltd. All rights reserved.