Principal eigenvalues for the weighted p-Laplacian and antimaximum principle in RN

We study the existence of principal eigenvalues and principal eigenfunctions for weighted eigenvalue problems of the form: {equation*} - div ( L (x) |∇ u|ᵖ⁻² ∇ u ) = λ K(x) |u|ᵖ⁻² u {.1cm} in {.1cm} R^N , {equation*} where λ ∈ R, $p>1$, K : RN → R, L : RN → R⁺ are locally integrable functions. The weight function K is allowed to change sign, provided it remains positive on a set of nonzero measure. We establish the existence, regularity, and asymptotic behavior of the principal eigenfunctions. We also prove local and global antimaximum principles for a perturbed version of the problem.