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This is a Quantitative Study study.

October 19, 2025Open Access

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

Key Points

Principal eigenvalues exist for weighted eigenvalue problems involving the weighted p-Laplacian.
Eigenfunctions demonstrate regularity and specific asymptotic behavior under conditions on weight functions.
Local and global antimaximum principles are established for a perturbed formulation of this eigenvalue problem.
Results indicate significant implications for the study of differential equations in R^N.

Abstract

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) = K (x) |u|^p-2 u. 1cm in. 1cm RN, equation* where 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.

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

Key Points

Abstract

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