Journal
ADVANCES IN CALCULUS OF VARIATIONS
Volume 9, Issue 2, Pages 101-125Publisher
WALTER DE GRUYTER GMBH
DOI: 10.1515/acv-2014-0024
Keywords
Fractional p-Laplacian problems; Morse theory; existence and multiplicity of weak solutions; regularity of solutions
Categories
Funding
- GNAMPA Project Problemi al contorno per operatori non locali non lineari
- National Natural Science Foundation of China [11171204]
- MIUR
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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.
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