Parametric Robin double phase problems with critical growth on the boundary

Giuseppina D'Aguì; Angela Sciammetta; Elisabetta Tornatore; Patrick Winkert

doi:10.3934/dcdss.2022156

Article Contents

2023, Volume 16, Issue 6: 1286-1299. Doi: 10.3934/dcdss.2022156

This issue Previous Article A competition on blow-up for semilinear wave equations with scale-invariant damping and nonlinear memory term Next Article Nonexistence results for nonlinear fractional differential inequalities involving weighted fractional derivatives

Parametric Robin double phase problems with critical growth on the boundary

1.
Department of Engineering, University of Messina, 98166 Messina, Italy
2.
Department of Mathematics and Computer Science, University of Palermo, 90123 Palermo, Italy
3.
Technische Universität Berlin, Institut für Mathematik, Straße des 17. Juni 136, 10623 Berlin, Germany

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

Received: June 2022

Revised: July 2022

Early access: August 2022

Published: June 2023

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Abstract

The aim of this paper is to study a double phase problem with nonlinear boundary condition of critical growth and with a superlinear right-hand side that does not satisfy the Ambrosetti-Rabinowitz condition. Based on an equivalent norm in the Musielak-Orlicz Sobolev space along with variational tools and critical point theory, we prove the existence of at least two nontrivial, bounded weak solutions.

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Mathematics Subject Classification: 35A01, 35J15, 35J62, 35J66.

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References

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