Existence of Solutions for a Quasilinear Reaction Diffusion System. (24th June 2012)

• Record Type: Journal Article
• Authors: Tian, Canrong
• Other Names: Anderson D. Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2012(2012)
• Publication Date: 2012-06-24
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2012/368425
• Languages: English
• ISSNs: 1085-3375

Abstract

Abstract : The degenerate reaction diffusion system has been applied to a variety of physical and engineering problems. This paper is extended the existence of solutions from the quasimonotone reaction functions (e.g., inhibitor-inhibitor mechanism) to the mixed quasimonotone reaction functions (e.g., activator-inhibitor mechanism). By Schauder fixed point theorem, it is shown that the system admits at least one positive solution if there exist a coupled of upper and lower solutions. This result is applied to a Lotka-Volterra predator-prey model.