Work

An eigenvalue problem for a generalized polyharmonic operator in Orlicz-Sobolev spaces without the $Δ_2$-condition

Year: 2026

Type: preprint

Abstract: In this paper, we consider a generalized polyharmonic eigenvalue problem of the form $A(u)= λh(u)$ in a bounded smooth domain with Dirichlet boundary conditions in the setting of higher-order Orlicz-Sobolev spaces. Here, $A$ is a very general operator depending on $u$ and arbitrary higher-order derivatives of $u$, whose growth is governed by an Orlicz function, and $h$ is a lower order term. Combining the theories of pseudomonotone operators with complementary systems, we prove that this eigenvalue problem has an infinite number of eigenfunctions and that the corresponding sequence of eigenvalues tends to infinite. We point out that the $Δ_2$-condition is not assumed for the involved Orlicz functions.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2602.10077

Authors: Dussel, Ignacio Ceresa, Bonder, Julián Fernández, Ochoa, Pablo

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, Universidad de Buenos Aires, Secretaría de Ciencia y Técnica, Universidad de Buenos Aires

Awards: G1767157483, G2439265903, G3097449728, G5925984592

OpenAlex ID: W7128628069

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