Multiplicity of clines for systems of indefinite differential equations arising from a multilocus population genetics model. (August 2020)

• Record Type: Journal Article
• Authors: Feltrin, Guglielmo; Gidoni, Paolo
• Is Part Of: Nonlinear analysis. Volume 54(2020)
• Publication Date: 2020-08
• Subjects: Neumann problem -- Indefinite weight -- Coincidence degree -- Multiplicity of clines -- Population genetics models -- Multilocus models; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2020.103108
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: We investigate sufficient conditions for the presence of coexistence states for different genotypes in a diploid diallelic population with dominance distributed on a heterogeneous habitat, considering also the interaction between genes at multiple loci. In mathematical terms, this corresponds to the study of the Neumann boundary value problem p 1 ′ ′ + λ 1 w 1 ( x, p 2 ) f 1 ( p 1 ) = 0, in Ω, p 2 ′ ′ + λ 2 w 2 ( x, p 1 ) f 2 ( p 2 ) = 0, in Ω, p 1 ′ = p 2 ′ = 0, on ∂ Ω, where the coupling-weights w i are sign-changing in the first variable, and the nonlinearities f i : [ 0, 1 ] → [ 0, + ∞ [ satisfy f i ( 0 ) = f i ( 1 ) = 0, f i ( s ) > 0 for all s ∈ ] 0, 1 [, and a superlinear growth condition at zero. Using a topological degree approach, we prove existence of 2 N positive fully nontrivial solutions when the real positive parameters λ 1 and λ 2 are sufficiently large.