The aim of this paper is to study a double phase problem with nonlinear boundary condition of critical growth and with a superlinear righthand 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.
Giuseppina D'Aguì, A.S. (2023). PARAMETRIC ROBIN DOUBLE PHASE PROBLEMS WITH CRITICAL GROWTH ON THE BOUNDARY. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES S, 16(6), 1286-1299 [10.3934/dcdss.2022156].
PARAMETRIC ROBIN DOUBLE PHASE PROBLEMS WITH CRITICAL GROWTH ON THE BOUNDARY
Angela Sciammetta;Elisabetta Tornatore;Patrick Winkert
2023-06-01
Abstract
The aim of this paper is to study a double phase problem with nonlinear boundary condition of critical growth and with a superlinear righthand 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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