Weighted p-Laplacian problems on a half-line

We study the weighted half-line eigenvalue problem -(vertical bar y'(x)vertical bar(p-1) sgn y'(x))' = (p - 1)(lambda r(x) - q(x))vertical bar y(x)vertical bar(p-1) sgn y(x), 0 <= x < infinity, for 1 < p < infinity, with initial condition y'(0) sin alpha = y(0) cos alpha, alpha is an element of [0, pi), using a modified Prufer angle phi(lambda, x). The eigenvalues lambda(k), k >= 0, with lambda(k) -> infinity as k -> infinity, are characterized by phi(lambda(k), x) -> (k +1)pi(p)-, and phi(lambda, x) -> (k + 1)pi(p)+ if lambda(k) < lambda < lambda(k+1), as x -> infinity. We allow the weight r to be locally integrable and definite, semidefinite or indefinite. In the first two cases, the sequence of eigenvalues accumulates at one of +/-infinity, and in the third, the sequence accumulates at both +/-infinity. In all cases, solutions y are nonoscillatory on (0, infinity) for all lambda. (C) 2015 Elsevier Inc. All rights reserved.