Article Contents

2024, Volume 23, Issue 9: 1325-1339. Doi: 10.3934/cpaa.2024058

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Logarithmic double phase problems with convection: existence and uniqueness results

Francesca Vetro^1, and
Patrick Winkert^2, ,

1.
Independent Researcher, Palermo, 90100, Italy
2.
Technische Universität Berlin, Institut für Mathematik, Straße des 17. Juni 136, 10623 Berlin, Germany

^*Corresponding author: Patrick Winkert
^*Corresponding author: Patrick Winkert

Received: April 2024

Revised: July 2024

Early access: July 2024

Published: September 2024

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Abstract

In this paper, we deal with a problem driven by a logarithmic double phase operator with variable exponent and a nonlinearity on the right-hand side which also depends on the gradient of the solution. Under very general structure conditions, following a topological approach based on the use of pseudomonotone operators, we establish the existence of a nontrivial weak solutions for the problem under consideration. Moreover, imposing more restrictive conditions on the nonlinearity, we are able to provide the uniqueness of the solution. Finally, we prove the boundedness, closedness and compactness of the related solution set to our problem.

Keywords:

Mathematics Subject Classification: Primary: 35A01, 35A16; Secondary: 35J62.

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