Work

Multiplicity results for logarithmic double phase problems via Morse theory

Year: 2025

Type: article

Abstract: In this paper, we study elliptic equations of the form where is the logarithmic double phase operator given by is Euler's number, , , is a bounded domain with Lipschitz boundary , , with , and . Under mild assumptions on the nonlinearity we prove multiplicity results for the problem above and get two constant sign solutions and another third nontrivial solution. This third solution is obtained by using the theory of critical groups. As a result of independent interest, we show that every weak solution of the problem above is essentially bounded.

Source: Bulletin of the London Mathematical Society

DOI: 10.1112/blms.70190

Authors: Vicenţiu D. Rădulescu, Matheus F. Stapenhorst, Patrick Winkert

Institutions: IMAR - Institutul de Matematică „Simion Stoilow” al Academiei Române, Brno University of Technology, AGH University of Krakow, 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: $3,930

Funder: Fundação de Amparo à Pesquisa do Estado de São Paulo