A double phase problem with a nonlinear boundary condition

Choudhuri, Debajyoti (author), Repovš, Dušan (author), Saoudi, Kamel (author)

In this paper we prove the existence of solutions to a double phase problem with a prescribed nonlinear boundary condition which is nonlinear in nature. The driving nonlinear perturbations obey a suitable condition at the origin and on the boundary. To the best of our knowledge, a double phase measure data problem with nonlinear boundary condition is new and has not been studied yet. The novelty of our work lies in using the well known weak convergence method to guarantee the existence of solutions. We also provide an illustrative example.

• Language: English
• Keywords: variable exponent Sobolev space, double phase operator, nonlinear boundary condition, Steklov eigenvalue problem, Robin eigenvalue problem, existence
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: PEF - Faculty of Education; FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Author Accepted Manuscript
• Publication date: 01.07.2023
• Year: 2023
• Number of pages: 17 str.
• Numbering: Vol. 46, iss. 4, art. 121
• PID: 20.500.12556/RUL-146155
• UDC: 517.9
• ISSN on article: 0126-6705
• DOI: 10.1007/s40840-023-01513-2
• COBISS.SI-ID: 152552963
• Publication date in RUL: 22.05.2023

Record is a part of a journal

• Title: Bulletin of the Malaysian Mathematical Sciences Society
• Shortened title: Bull. Malays. Math. Sci. Soc.
• Publisher: Springer Nature, Malaysian Mathematical Sciences Society, Penerbit Universiti Sains Malaysia
• ISSN: 0126-6705
• COBISS.SI-ID: 515781657