Premium
Fractional weighted problems with a general nonlinearity or with concave‐convex nonlinearities
Author(s) -
Appolloni Luigi,
Mugnai Dimitri
Publication year - 2021
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.7515
Subject(s) - mathematics , eigenvalues and eigenvectors , nonlinear system , regular polygon , operator (biology) , concave function , sign (mathematics) , mathematical analysis , geometry , biochemistry , chemistry , physics , repressor , quantum mechanics , transcription factor , gene
We consider nonlocal problems in which the leading operator contains a sign‐changing weight which can be unbounded. We begin studying the existence and the properties of the first eigenvalue. Then we study a nonlinear problem in which the nonlinearity does not satisfy the usual Ambrosetti‐Rabinowitz condition. Finally, we study a problem with general concave‐convex nonlinearities.