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math.AP2021★ 4 cited
Confining integro-differential equations originating from evolutionary biology: ground states and long time dynamics
Matthieu Alfaro, Pierre Gabriel, Otared Kavian
We consider nonlinear mutation selection models, known as replicator-mutator equations in evolutionary biology. They involve a nonlocal mutation kernel and a confining fitness pote…
math.AP2015
The Fokker-Planck equation with subcritical confinement force
Otared Kavian, Stéphane Mischler, Mamadou Ndao
We consider the Fokker-Planck equation with subcritical confinement force field which may not derive from a potential function. We prove the existence of an equilibrium (in the cas…
math.AP2013
A global approach to the Schrödinger-Poisson system: An Existence result in the case of infinitely many states
Otared Kavian, Stéphane Mischler
In this paper we prove the existence of a solution to a nonlinear Schr{ö}dinger--Poisson eigenvalue problem in dimension less than . Our proof is based on a global approach to t…