WIAS Preprint No. 1963, (2014)
Asymptotically linear problems driven by fractional Laplacian operators
- Fiscella, Alessio
- Servadei, Raffaella
- Valdinoci, Enrico
2010 Mathematics Subject Classification
- 49J35 35A15 35S15 47G20 45G05
- Integrodifferential operators, fractional Laplacian, variational techniques, Saddle Point Theorem, Palais-Smale condition
In this paper we study a non-local fractional Laplace equation, depending on a parameter, with asymptotically linear right-hand side. Our main result concerns the existence of weak solutions for this equation and it is obtained using variational and topological methods. We treat both the nonresonant case and the resonant one.
- Math. Methods Appl. Sci., 38 (2015) pp. 3551--3563.