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.
Appolloni, L., Mugnai, D. (2021). Fractional weighted problems with a general nonlinearity or with concave-convex nonlinearities. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 44(14), 11571-11590 [10.1002/mma.7515].
Fractional weighted problems with a general nonlinearity or with concave-convex nonlinearities
Appolloni L.;
2021
Abstract
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.
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