Positive periodic solutions to a system of nonlinear differential equations with applications to Lotka–Volterra-type ecological models with discrete and distributed delays

2019 ◽  
Vol 21 (3) ◽  
Author(s):  
Smita Pati ◽  
John R. Graef ◽  
Seshadev Padhi
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Nonlinear Differential Equations ◽  
Ecological Models ◽  
Distributed Delays ◽  
Positive Periodic Solutions ◽  
Volterra Type

THREE POSITIVE PERIODIC SOLUTIONS OF NONLINEAR DIFFERENTIAL EQUATIONS WITH PERIODIC COEFFICIENTS

2005 ◽  
Vol 03 (02) ◽  
pp. 145-155 ◽  
Author(s):  
YUJI LIU ◽  
WEIGUO GE ◽  
ZHANJI GUI
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Order Differential Equation ◽  
Nonlinear Differential Equations ◽  
Second Order ◽  
Positive Periodic Solutions ◽  
Periodic Coefficients ◽  
Second Order Differential Equation

We establish the existence of at least three positive periodic solutions to the second order differential equation with periodic coefficients [Formula: see text] where f is continuous with f(t + T, x) = f(t,x) for (t,x) ∊ R × R and T > 0, p, q are continuous and T-periodic with p > 0 and q ≥ 0. We accomplish this by making growth assumptions on f, which can apply to many more cases than those discussed in recent works. An example to illustrate the main result is given.

scholarly journals Multiplicity of positive periodic solutions to second order differential equations

2006 ◽  
Vol 73 (2) ◽  
pp. 175-182 ◽  
Author(s):  
Jifeng Chu ◽  
Xiaoning Lin ◽  
Daqing Jiang ◽  
Donal O'Regan ◽  
R. P. Agarwal
Keyword(s):  
Periodic Solution ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Point Theorem ◽  
Positive Periodic Solution ◽  
Second Order ◽  
Positive Periodic Solutions ◽  
Second Order Differential Equations

In this paper, we study the existence of positive periodic solutions to the equation x″ = f (t, x). It is proved that such a equation has more than one positive periodic solution when the nonlinearity changes sign. The proof relies on a fixed point theorem in cones.

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