Work

Critical logarithmic double phase problems of Brezis–Nirenberg type with nonlinear boundary condition

Year: 2026

Type: article

Abstract: In this paper, we investigate the existence and multiplicity of solutions to a class of nonlinear elliptic problems governed by the logarithmic double phase operator and subject to nonlinear critical Neumann boundary conditions. By employing variational methods in combination with topological tools such as truncation techniques and Krasnosel’skii’s genus theory, we establish the existence of infinitely many weak solutions with negative energy sign. The results highlight the rich solution structure arising from the interplay between the logarithmic double phase operator and the critical boundary growth.

Source: Zeitschrift für angewandte Mathematik und Physik

DOI: 10.1007/s00033-026-02770-4

Authors: Yino B. Cueva Carranza, Marcos T. O. Pimenta, Patrick Winkert

Institutions: Universidade Estadual Paulista (Unesp), Technische Universität Berlin

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,590

Funders: Fundação de Amparo à Pesquisa do Estado de São Paulo, Conselho Nacional de Desenvolvimento Científico e Tecnológico, Technische Universität Berlin