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 dierent 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.
Iannizzotto, A., Liu, S., Perera, K., Squassina, M., Existence results for fractional p-Laplacian problems via Morse theory, <<ADVANCES IN CALCULUS OF VARIATIONS>>, 2016; 9 (N/A): 101-125. [doi:10.1515/acv-2014-0024] [http://hdl.handle.net/10807/87083]
Existence results for fractional p-Laplacian problems via Morse theory
Squassina, MarcoUltimo
2016
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 dierent 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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