Arbitrarily small nodal solutions for nonhomogeneous Robin problems

Article type: Research Article

Authors: Zeng, Shengda^{a; b; *} | Papageorgiou, Nikolaos S.^c

Affiliations: [a] Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing, Yulin Normal University, Yulin 537000, Guangxi, P.R. China | [b] Faculty of Mathematics and Computer Science, Jagiellonian University in Krakow, ul. Lojasiewicza 6, 30-348 Krakow, Poland | [c] Department of Mathematics, National Technical University, Zograrou Compus, Athens 15780, Greece

Correspondence: [*] Corresponding author. Tel.: +86-18059034172; E-mail: [email protected].

Abstract: In the present paper, we consider a nonlinear Robin problem driven by a nonhomogeneous differential operator and with a reaction which is only locally defined. Using cut-off techniques and variational tools, we show that the problem has a sequence of nodal solutions converging to zero in C1(Ω‾).

Keywords: Nonhomogeneous differential operator, locally defined reaction, cut-off function, extremal constant sign solution, nodal solution

DOI: 10.3233/ASY-211716

Journal: Asymptotic Analysis, vol. 128, no. 4, pp. 539-553, 2022