Invasion entire solutions for two-species diffusive monostable competitive systems. (June 2021)

• Record Type: Journal Article
• Authors: Salako, Rachidi B.
• Is Part Of: Nonlinear analysis. Volume 59(2021)
• Publication Date: 2021-06
• Subjects: Reaction–diffusion equations -- Competitive systems -- Entire solutions -- Traveling waves; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2020.103264
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: We study the existence of entire solutions of two-species diffusive monostable Lotka–Volterra competitive systems. Our results cover both cases of monostable with stable coexistence equilibrium and monostable with competition–extinction equilibria. We prove the existence of entire solutions describing different types of invasion scenarios of an empty territory by two competitors as the time variable t → − ∞ . Depending on the mobile species, these invasion phenomena can occur either from one side or both sides of the x -axis, leading to the existence of different types of entire solutions. In particular, the existence of entire solution characterizing the invasion of an empty habitat from one side by a weaker competitor and from both sides of the same territory by a stronger competitor as the time variable t → − ∞ are established. We construct delicate super–sub solutions and employ the comparison principle to prove our main results.