On the eigenvalue problem involving the weighted p-Laplacian in radially symmetric domains

We investigate the following eigenvalue problem {-div (L(x) vertical bar del u vertical bar(p-2)del u) = lambda K(x)vertical bar u vertical bar(p-2)u in A(R1)(R2), u = 0 on partial derivative A(R1)(R2), where A(R1)(R2) := {x is an element of R-N : R1 < vertical bar x vertical bar < R-2} (0 < R-1 < R-2 <= infinity), lambda > 0 is a parameter, the weights L and K are measurable with L positive a.e. in A(R1)(R2) and K possibly sign-changing in A(R1)(R2). We prove the existence of the first eigenpair and discuss the regularity and positiveness of eigenfunctions. The asymptotic estimates for u(x) and del u(x) as vertical bar x vertical bar -> R-1(+) or R-2(-) are also investigated. (C) 2018 Elsevier Inc. All rights reserved.