Nonlinear, nonhomogeneous Robin problems with indefinite potential and general reaction
ID Papageorgiou, Nikolaos S. (Author), ID Rǎdulescu, Vicenţiu (Author), ID Repovš, Dušan (Author)

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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.

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
Number of pages:Str. 823-857
Numbering:Vol. 81, iss. 3
PID:20.500.12556/RUL-116658 This link opens in a new window
ISSN on article:0095-4616
DOI:10.1007/s00245-018-9521-x This link opens in a new window
COBISS.SI-ID:18436441 This link opens in a new window
Publication date in RUL:01.06.2020
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Title:Applied mathematics and optimization
Shortened title:Appl. math. optim.
COBISS.SI-ID:24984064 This link opens in a new window

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