Special Session 93: Local and nonlocal elliptic boundary value problems

Morse-theoretic approach for logarithmic double phase problems
Patrick Winkert
University of Technology Berlin
Germany
Co-Author(s):    
Abstract:
In this talk, we investigate nonlinear elliptic problems involving logarithmic double phase operators and superlinear nonlinearities. Using critical group theory and variational methods, we show that the problem admits at least three distinct nontrivial bounded weak solutions. Two of these solutions have constant sign and positive energy, while a third is obtained via a topological argument involving the structure of the critical groups at zero and at infinity. This talk is based on joint works with Franziska Borer (Berlin), Vicen\c{t}iu D. R\u{a}dulescu (Krakow) and Matheus F. Stapenhorst (Presidente Prudente).