Communications - Scientific Letters of the University of Zilina 2014, 16(3):69-73 | DOI: 10.26552/com.C.2014.3.69-73
Existence of Positive Solutions of a Nonlinear Differential Equation with N Delays
- 1 Department of Mathematics, Faculty of Humanities, University of Zilina, Slovakia
The equation yt abty t i t n 1 i x=+a = o^^ ^^ hhhh % is considered where n is a positive integer, a,τi and αi,i = 1,2,...,n are positive constants and conditions on function b are formulated such that the considered equation has positive solutions when t → ∞. The equation is studied under assumptions,.ae 11 ii i n i i n 11 1 ax a = == cm // Estimation of positive solutions is given as well. The proof is based on the retract technique.
Keywords: nonlinear differential equation with delays, positive solutions, transcendental equation, asymptotic behavior
Published: July 31, 2014 Show citation
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References
- DIBLIK, J., RUZICKOVA, M.: Asymptotic Behavior of Solutions and Positive Solutions of Differential Delayed Equations, Funct. Differ. Equ. 14, No. 1, 2007, 83-105.
- AGARWAL, R. P., BEREZANSKY, L., BRAVERMAN, E., DOMOSHNITSKY, A.: Nonoscillation Theory of Functional Differential Equations with Applications, Springer, 2012.
Go to original source... - AGARWAL, R. P., BOHNER, M., WAN-TONG, LI.: Nonoscillation and Oscillation: Theory for Functional Differential Equations, Marcel Dekker, Inc. 2004. Go to original source...
- DRIVER, R. D.: Ordinary and Delay Differential Equations, Springer-Verlag, 1977. Go to original source...
- HALE, J. K., LUNEL, S. M. V.: Introduction to Functional Differential Equations, Springer-Verlag, 1993. Go to original source...
- DIBLIK, J.: A Criterion for Existence of Positive Solutions of Systems of Retarded Functional Differential Equations, Nonlinear Anal., 38, 1999, 327-339. Go to original source...
- DIBLIK, J., KOKSCH, N.: Positive Solutions of the Equation in the Critical Case, J. Math. Anal. Appl., 250, 2000, 635-659. Go to original source...
- DIBLIK, J., KUDELCIKOVA, M.: Existence and Asymptotic Behavior of Positive Solutions of Functional Differential Equations of Delayed Type, Abstr. and Appl. Anal., vol. 2011, 2011, 16 p. Go to original source...
- DIBLIK, J., RUZICKOVA, M, SMARDA, Z.: Wazewski's Method for Systems of Dynamic Equations on Time Scales, Nonlinear Anal., 71, 2009, E1124-E1131. Go to original source...
- Diblik, J., Svoboda, Z.: An Existence Criterion of Positive Solutions of p-type Retarded Functional Differential Equations, J. Comput. Appl. Math. 147, 2002, 315-331. Go to original source...
- DIBLIK J., SVOBODA Z.: Positive Solutions of Retarded Functional Differential Equations, Nonlinear Anal., 63, 2005, 813-821. Go to original source...
- DIBLIK, J., SVOBODA, Z.: Positive Solutions of type Retarded Functional Differential Equations, Nonlinear Anal., 64, 2006, 1831-1848. Go to original source...
- DOMOSHNITSKY, A., DRAKHLIN, M.: Nonoscillation of First Order Differential Equations with Delay, J. Math. Anal. Appl., 206, 1997, 254-269. Go to original source...
- SAMAJOVA, H., SPANIKOVA, E., Dix, J. G.: Decay of Non-oscillatory Solutions for a System of Neutral Differential Equations, Electron. J. Differential Equations, No 271, 2013, 2013, 1-11.
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