scholarly journals Non-trivial non-negative periodic solutions of a system of doubly degenerate parabolic equations with nonlocal terms

2011 ◽  
Vol 31 (1) ◽  
pp. 35-64 ◽  
Author(s):  
Genni Fragnelli ◽  
◽  
Paolo Nistri ◽  
Duccio Papini ◽  
◽  
...  
Keyword(s):  
Periodic Solutions ◽  
Parabolic Equations ◽  
Degenerate Parabolic Equations ◽  
Degenerate Parabolic ◽  
Nonlocal Terms

scholarly journals Nontrivial, nonnegative periodic solutions of a system of singular-degenerate parabolic equations with nonlocal terms

2015 ◽  
Vol 17 (02) ◽  
pp. 1450025 ◽  
Author(s):  
Genni Fragnelli ◽  
Dimitri Mugnai ◽  
Paolo Nistri ◽  
Duccio Papini
Keyword(s):  
Periodic Solutions ◽  
Parabolic Equations ◽  
Dirichlet Boundary ◽  
Degree Theory ◽  
Biological Species ◽  
Dirichlet Boundary Conditions ◽  
Degenerate Parabolic Equations ◽  
Topological Degree Theory ◽  
Degenerate Parabolic ◽  
Nonlocal Terms

We study the existence of nontrivial, nonnegative periodic solutions for systems of singular-degenerate parabolic equations with nonlocal terms and satisfying Dirichlet boundary conditions. The method employed in this paper is based on the Leray–Schauder topological degree theory. However, verifying the conditions under which such a theory applies is more involved due to the presence of the singularity. The system can be regarded as a possible model of the interactions of two biological species sharing the same isolated territory, and our results give conditions that ensure the coexistence of the two species.

Coexistence Solutions for a Periodic Competition Model with Singular–Degenerate Diffusion

2016 ◽  
Vol 60 (4) ◽  
pp. 1065-1075
Author(s):  
Yifu Wang ◽  
Jingxue Yin ◽  
Yuanyuan Ke
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Periodic Solutions ◽  
Parabolic Equations ◽  
Competition Model ◽  
Degenerate Parabolic Equations ◽  
Degenerate Diffusion ◽  
Volterra Type ◽  
Non Local ◽  
Degenerate Parabolic

AbstractWe investigate a system of singular–degenerate parabolic equations with non-local terms, which can be regarded as a spatially heterogeneous competition model of Lotka–Volterra type. Applying the Leray–Schauder fixed-point theorem, we establish the existence of coexistence periodic solutions to the problem, which, together with the existing literature, gives a complete picture for such a system for all parameters.

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