Affiliations: [a] Department of Mathematics, Zografou campus, National Technical University, 15780, Athens, Greece. E-mail: [email protected] | [b] Department of Mathematics and Computer Science, University of Palermo, Via Archirafi 34, 90123, Palermo, Italy. E-mail: [email protected] | [c] Nonlinear Analysis Research Group, Ton Duc Thang University, Ho Chi Minh City, Vietnam | [d] Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam. E-mail: [email protected]
Abstract: We consider a parametric double phase problem with Robin boundary condition. We prove two existence theorems. In the first the reaction is (p−1)-superlinear and the solutions produced are asymptotically big as λ→0+. In the second the conditions on the reaction are essentially local at zero and the solutions produced are asymptotically small as λ→0+.
Keywords: Unbalanced growth, asymptotically big solutions, asymptotically small solutions, superlinear reaction, C-condition
