Existence and Mann iterative methods of positive solutions of first order nonlinear neutral difference equations
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In this paper, we study the first order nonlinear neutral difference equation:Δ(x(n)+px(n-Τ))+f(n,x(n-c),x(n-d))=r(n), n≥n_0. Using the Banach fixed point theorem, we prove the existence of bounded positive solutions of the equation, suggest Mann iterative schemes of bounded positive solutions, and discuss the error estimates between bounded positive solutions and sequences generated by Mann iterative schemes.
Abstract
In this paper, we study the first order nonlinear neutral difference equation:Δ(x(n)+px(n-Τ))+f(n,x(n-c),x(n-d))=r(n), n≥n_0. Using the Banach fixed point theorem, we prove the existence of bounded positive solutions of the equation, suggest Mann iterative schemes of bounded positive solutions, and discuss the error estimates between bounded positive solutions and sequences generated by Mann iterative schemes.
참고문헌 (4)
- R. P. Agarwal, "Difference Equations and Inequalities, Second Edition" (2000), Marcel Dekker
- M. P. Chen, "Oscillation and comparison theorems of difference equations with positive and negative coefficients", Bull. Inst. Math. Acad. Sin. (N.S.), 22, pp.295~306 (1994)
- B. S. Lalli, "On existence of positive solutions and bounded oscillations for neutral difference equations", J. Math. Anal. Appl., 166, pp.272~287 (1992)
- B. G. Zhang, "The existence of oscillatory and nonoscillatory solution of neutral difference equation", Chinese J. Math., 24, pp.377~393 (1996)