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Positive Periodic Solutions of Neutral Functional Differential Equations with State Dependent Delays on Time Scales

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Abstract:

By using a fixed point theorem on strict-set-contraction, some sufficient conditions are obtained for the existence of positive periodic solutions for a periodic neutral functional differential equation on time scales of the form
x^Δ(t)=x(t)[r(t)-a(t)x(t)-∑ⁿ_j₌₁a_j(t) x(t-τ_j(t, x(t)))-∑ⁿ_j₌₁c_j(t) x^Δ(t-σ_j(t, x(t)))g ],
where r, a, a_j, c_j∈C( T, R⁺)(j =1, 2, … , n) are ω -periodic functions, and τ_j, σ_j∈C( T×R, T)(j =1, 2, … , n) are ω -periodic functions with respect to their first arguments, respectively.

Key words: Positive periodic solution, Neutral functional differential equation, Time scales, Strict-set-contraction

CLC Number:

34K13

LI Yong-Kun, ZHANG Hong-Tao. Positive Periodic Solutions of Neutral Functional Differential Equations with State Dependent Delays on Time Scales[J].Acta mathematica scientia,Series A, 2010, 30(3): 730-742.

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[1] Lu S. On the existence of positive periodic solutions for neutral functional differential equation with multiple deviating arguments. J Math Anal Appl, 2003, 280: 321--333

[2] Kuang Y, Feldstein A. Boundedness of solutions of a nonlinear nonautonomous neutral delay equation. J Math Anal Appl, 1991, 156: 293--304

[3] Gopalsamy K, He X, Wen L. On a periodic neutral logistic equation. Glasgow Math J, 1991, 33: 281--286

[4] Gopalsamy K, Zhang B G. On a neutral delay logistic equation. Dynam Stability Systems, 1988, 2: 183--195

[5] Pielou E C. Mathematics Ecology. New York: Wiley-Interscience, 1977

[6] Chen F, Lin F, Chen X. Sufficient conditions for the existence positive periodic solutions of a clas s of neutral delay models with feedback control. Appl Math Comput, 2004, 158(1): 45--68

[7] Yang Z, Cao J. Existence of periodic solutions in neutral state-dependent delays equations and models. J Comput Appl Math, 2005, 174: 179--199

[8] Gaines R E, Mawhin J L. Lecture Notes in Mathematics. Berlin: Springer-Verlag, 1977

[9] Cäc N P, Gatica J A. Fixed point theorems for mappings in ordered Banach spaces. J Math Anal Appl, 1979, 71: 547--557

[10] Kaufmann E R, Raffoul Y N. Periodic solutions for a neutral nonlinear dynamical equation on a time scale. J Math Anal Appl, 2006, 319: 315--325

[11] Bohner M, Peterson A. Dynamic Equations on Time Scales. An Introduction with Applications. Boston: Birkhä}user, 2001

[12] Guo D. Positive solutions of nonlinear operator equations and its applications to nonlinear integral equations. Adv Math, 1984, 13: 294--310 (in Chinese)

[13] Xing Y, Han M, Zheng G. Initial value problem for first-order integro-differential equation of Volterra type on time scales. Nonlinear Anal, 2005, 60: 429--442

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