Solutions for parametric double phase Robin problems

Article type: Research Article

Authors: Papageorgiou, Nikolaos S.^a | Vetro, Calogero^{b; *} | Vetro, Francesca^{c; d}

Affiliations: [a] Department of Mathematics, Zografou campus, National Technical University, 15780, Athens, Greece. E-mail: npapg@math.ntua.gr | [b] Department of Mathematics and Computer Science, University of Palermo, Via Archirafi 34, 90123, Palermo, Italy. E-mail: calogero.vetro@unipa.it | [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: francescavetro@tdtu.edu.vn

Correspondence: [*] Corresponding author. E-mail: calogero.vetro@unipa.it.

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

DOI: 10.3233/ASY-201598

Journal: Asymptotic Analysis, vol. 121, no. 2, pp. 159-170, 2021