Stationary solutions of Fokker-Planck equations with nonlinear reaction terms in bounded domains


Using an operator approach, we discuss stationary solutions to Fokker-Planck equations and systems with nonlinear reaction terms. The existence of solutions is obtained by using Banach, Schauder and Schaefer fixed point theorems, and for systems by means of Perov’s fixed point theorem. Using the Ekeland variational principle, it is proved that the unique solution of the problem minimizes the energy functional, and in case of a system that it is the Nash equilibrium of the energy functionals associated to the component equations.


Radu Precup
Department of Mathematics Babes-Bolyai University, Cluj-Napoca, Romania

Paola Rubbioni
Department of Mathematics and Computer Science, University of Perugia, Perugia, Italy


Elliptic equation; Reaction-diffusion equation; Semi-linear Fokker-Planck equation; Fixed point; Variational method; Nash type equilibrium

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R. Precup, P. Rubbioni, Stationary solutions of Fokker-Planck equations with nonlinear reaction terms in bounded domains, Potential Analysis, 57 (2022), 181–199,



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