Work

Nonlinear eigenvalue problems for a biharmonic operator in Orlicz–Sobolev spaces

Year: 2025

Type: article

Abstract: In this paper, we study a higher‐order Laplacian operator in the framework of Orlicz–Sobolev spaces, the biharmonic g ‐Laplacian where , with being an N ‐function. This operator is a generalization of the so‐called bi‐harmonic Laplacian . Here, we also establish basic functional properties of , which can be applied to existence results. Afterwards, we study the eigenvalues of , which depend on normalization conditions, due to the lack of homogeneity of the operator. Finally, we study different nonlinear eigenvalue problems associated to and we show regimes where the corresponding spectrum concentrates at 0, or coincide with .

Source: Mathematische Nachrichten

DOI: 10.1002/mana.70087

Authors: Pablo Ochoa, Analía Silva

Institutions: Consejo Nacional de Investigaciones Científicas y Técnicas, Universidad Nacional de Cuyo, National University of San Luis

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Consejo Nacional de Investigaciones Científicas y Técnicas, Agencia Nacional de Promoción Científica y Tecnológica, Fondo para la Investigación Científica y Tecnológica