Multiple solutions to logarithmic double phase problems involving superlinear nonlinearities
Abstract
This paper investigates a class of problems involving a logarithmic double phase operator with variable exponents and right-hand sides that consist of nonlinearities exhibiting subcritical and superlinear growth. Under very general assumptions, we prove the existence of at least two nontrivial bounded weak solutions for such problems whereby the solutions have opposite energy sign. In addition, we give conditions on the nonlinearity under which the solutions turn out to be nonnegative.
Fields of Study & Subjects
Nonlinear Partial Differential Equations
Solidification and crystal growth phenomena
Nonlinear Differential Equations Analysis
Publication details
- Journal / source
- Zeitschrift für Analysis und ihre Anwendungen
- Publisher
- European Mathematical Society - EMS - Publishing House GmbH
- Publication date
- 8 January 2026