Nonlinear, nonhomogeneous Robin problems with indefinite potential and general reaction

Papageorgiou, Nikolaos S. (author), Rǎdulescu, Vicenţiu (author), Repovš, Dušan (author)

We consider a nonlinear elliptic equation driven by a nonhomogeneous differential operator plus an indefinite potential. On the reaction term we impose conditions only near zero. Using variational methods, together with truncation and perturbation techniques and critical groups, we produce three nontrivial solutions with sign information. In the semilinear case we improve this result by obtaining a second nodal solution for a total of four nontrivial solutions. Finally, under a symmetry condition on the reaction term, we generate a whole sequence of distinct nodal solutions.

• Language: English
• Keywords: nonhomogeneous differential operator, nonlinear regularity theory, constant sign and nodal solutions, infinitely many nodal solutions, critical groups
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: PEF - Faculty of Education; FMF - Faculty of Mathematics and Physics
• Year: 2020
• Number of pages: Str. 823-857
• Numbering: Vol. 81, iss. 3
• PID: 20.500.12556/RUL-116658
• UDC: 517.956.2
• ISSN on article: 0095-4616
• DOI: 10.1007/s00245-018-9521-x
• COBISS.SI-ID: 18436441
• Publication date in RUL: 01.06.2020

Record is a part of a journal

• Title: Applied mathematics and optimization
• Shortened title: Appl. math. optim.
• Publisher: Springer.
• ISSN: 0095-4616
• COBISS.SI-ID: 24984064