Abstract
We investigate a class of quasi-linear nonlocal problems, including as a particular case semi-linear problems involving the fractional Laplacian and arising in the framework of continuum mechanics, phase transition phenomena, population dynamics and game theory. Under different growth assumptions on the reaction term, we obtain various existence as well as finite multiplicity results by means of variational and topological methods and, in particular, arguments from Morse theory.
Funding source: GNAMPA
Award Identifier / Grant number: Problemi al contorno per operatori non locali non lineari
Funding source: National Natural Science Foundation of China
Award Identifier / Grant number: 11171204
Funding source: MIUR
Award Identifier / Grant number: Variational and Topological Methods in the Study of Nonlinear Phenomena
The authors would like to thank Xavier Ros-Oton for precious bibliographic information on the regularity up to the boundary of the solutions to the problem, as well as Sun-Ra Mosconi for some useful remarks concerning Section 5.
© 2016 by De Gruyter