We consider the following Liouville-type PDE, which is related to stationary solutions of the Keller-Segel's model for chemotaxis: (Equation Presented) where Ω ⊂ ℝ2 is a smooth bounded domain and β, ρ are real parameters. We prove existence of solutions under some algebraic conditions involving β, ρ. In particular, if Ω is not simply connected, then we can find solution for a generic choice of the parameters. We use variational and Morse-theoretical methods.
Battaglia, L. (2019). A general existence result for stationary solutions to the Keller-Segel system. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 39(2), 905-926 [10.3934/dcds.2019038].
A general existence result for stationary solutions to the Keller-Segel system
Battaglia, Luca
2019-01-01
Abstract
We consider the following Liouville-type PDE, which is related to stationary solutions of the Keller-Segel's model for chemotaxis: (Equation Presented) where Ω ⊂ ℝ2 is a smooth bounded domain and β, ρ are real parameters. We prove existence of solutions under some algebraic conditions involving β, ρ. In particular, if Ω is not simply connected, then we can find solution for a generic choice of the parameters. We use variational and Morse-theoretical methods.| File | Dimensione | Formato | |
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