Three positive periodic solutions to nonlinear neutral functional differential equations with impulses and parameters on time scales

In this paper, using the Leggett-Williams fixed point theorem, we investigate the existence of three positive periodic solutions to the nonlinear neutral functional differential equations with impulses and parameters on time scales {(x(t)+c(t)x(t-r"1))^@D=a(t)g(x(t))x(t)-@?i=1n@l"if"i(t,x(t-@t"i(t))),t t"j,t@?T,j=1,2,...,q,x(tj-)-x(tj+)=I"j(x(t"j)),t=t"j,j=1,2,...,q, where @l"i, i=1,2,...,n are parameters, T is an @w-periodic time scale, a@?C(T,R^+),c@?C(T,[0,1)) and both of them are @w-periodic functions, @t"i@?C(T,R),i=1,2,...,n are@w-periodic functions, f"i@?C(TxR^+,R^+),i=1,2,...,n are nondecreasing with respect to their second arguments and @w-periodic with respect to their first arguments, respectively; g@?C(R^+,R^+) and there exist two positive constants l,L such that 00,I"j@?C(R,R^+)(j=1,2,...,q) and is bounded, r"1 is a constant.

[1]  G. M.,et al.  Partial Differential Equations I , 2023, Applied Mathematical Sciences.

[2]  Amos Gilat,et al.  Matlab, An Introduction With Applications , 2003 .

[3]  Johnny Henderson,et al.  Double Solutions of Impulsive Dynamic Boundary Value Problems on a Time Scale , 2002 .

[4]  Binxiang Dai,et al.  Three periodic solutions of nonlinear neutral functional differential equations , 2008 .

[5]  Enrico Serra,et al.  Periodic solutions for some nonlinear differential equations of neutral type , 1991 .

[6]  A. Peterson,et al.  Dynamic Equations on Time Scales , 2001 .

[7]  A. Peterson,et al.  Dynamic Equations on Time Scales: An Introduction with Applications , 2001 .

[8]  Yuexiang Wu,et al.  Existence of positive periodic solutions for a functional differential equation with a parameter , 2008 .

[9]  Yang Kuang,et al.  Periodic Solutions of Periodic Delay Lotka–Volterra Equations and Systems☆ , 2001 .

[10]  Ping Liu,et al.  Positive periodic solutions of infinite delay functional differential equations depending on a parameter , 2004, Appl. Math. Comput..

[11]  R. Leggett,et al.  Multiple positive fixed points of nonlinear operators on ordered Banach spaces , 1979 .

[12]  Fengxiang,et al.  POSITIVE PERIODIC SOLUTIONS OF NONLINEAR FUNCTIONAL DIFFERENCE EQUATION , 2006 .

[13]  Ethelbert N. Chukwu,et al.  Evolution equations of Lurie-type in Hilbert spaces , 1985 .

[14]  Paul W. Eloe,et al.  The quasilinearization method for boundary value problems on time scales , 2002 .

[15]  Guang Zhang,et al.  Existence of Positive Periodic Solutions for Non-Autonomous Functional Differential Equations , 2001 .

[16]  Haiyan Wang.  Positive periodic solutions of functional differential equations , 2004 .

[17]  Yepeng Xing,et al.  Initial value problem for first-order integro-differential equation of Volterra type on time scales , 2005 .