On non-autonomous linear difference equations with continuous variable

References

• Agarwal , R.P. 1992 . Difference Equations and Inequalities , New York : Marcel Dekker .
   Google Scholar
• Arino , O. and Pituk , M. 2001 . More on linear differential systems with small delays . Journal of Differential Equations , 170 : 381 – 407 .
   Web of Science ®Google Scholar
• de Bruijn , N.G. 1950 . On some linear functional equations . Publicationes Mathematicae Debrecen , 1 : 129 – 134 .
   Google Scholar
• Dix , J.G. , Philos , Ch.G. and Purnaras , I.K. 2005 . An asymptotic property of solutions to linear non-autonomous delay differential equations . Electronic Journal of Differential Equations , 2005 ( No. 10 ) : 1 – 9 .
   Google Scholar
• Dix, J.G., Philos, Ch.G. and Purnaras, I.K., 2006, Asymptotic properties of solutions to linear non-autonomous neutral differential equations. Journal of Mathematical Analysis and Applications, 318, 296–304.
   Google Scholar
• Domshlak , Y. 1993 . Oscillatory properties of linear difference equations with continuous time . Differential Equations and Dynamical Systems , 1 : 311 – 324 .
   Google Scholar
• Driver , R.D. 1972 . “ Some harmless delays ” . In Delay and Functional Differential Equations and Their Applications , 103 – 119 . New York : Academic Press .
   Google Scholar
• Driver , R.D. 1976 . Linear differential systems with small delays . Journal of Differential Equations , 21 : 148 – 166 .
   Web of Science ®Google Scholar
• Driver , R.D. , Ladas , G. and Vlahos , P.N. 1992 . Asymptotic behavior of a linear delay difference equation . Proceedings of the American Mathematical Society , 115 : 105 – 112 .
   Web of Science ®Google Scholar
• Driver , R.D. , Sasser , D.W. and Slater , M.L. 1973 . The equation x′(t)=ax(t)+bx(t − τ) with “small” delay . American Mathematical Monthly , 80 : 990 – 995 .
   Web of Science ®Google Scholar
• Elaydi , S.N. 1996 . An Introduction to Difference Equations , New York : Springer .
   Google Scholar
• Frasson , M.V.S. and Verduyn Lunel , S.M. 2003 . Large time behaviour of linear functional differential equations . Integral Equations Operator Theory , 47 : 91 – 121 .
   Web of Science ®Google Scholar
• Graef , J.R. and Qian , C. 1998 . Asymptotic behavior of forced delay equations with periodic coefficients . Communications in Applied Analysis , 2 : 551 – 564 .
   Google Scholar
• Györi , I. 1990 . Invariant cones of positive initial functions for delay differential equations . Applicable Analysis , 35 : 21 – 41 .
   Google Scholar
• Györi , I. 1990 . Sharp conditions for existence of nontrivial invariant cones of nonnegative initial values of difference equations . Applied Mathematics and Computation , 36 : 89 – 111 .
   Web of Science ®Google Scholar
• Kelley , W.G. and Peterson , A.C. 1991 . Difference Equations: An Introduction with Applications , New York : Academic Press, Inc. .
   Google Scholar
• Kordonis , I.-G.E. , Niyianni , N.T. and Philos , Ch.G. 1998 . On the behavior of the solutions of scalar first order linear autonomous neutral delay differential equations . Archives of Mathematics (Basel) , 71 : 454 – 464 .
   Web of Science ®Google Scholar
• Kordonis , I.-G.E. and Philos , Ch.G. 1999 . The behavior of solutions of linear integro-differential equations with unbounded delay . Computers & Mathematics with Applications , 38 : 45 – 50 .
   Web of Science ®Google Scholar
• Kordonis , I.-G.E. and Philos , Ch.G. 1999 . On the behavior of the solutions for linear autonomous neutral delay difference equations . Journal of Difference Equations and Applications , 5 : 219 – 233 .
   Web of Science ®Google Scholar
• Kordonis , I.-G.E. , Philos , Ch.G. and Purnaras , I.K. 1998 . Some results on the behavior of the solutions of a linear delay difference equation with periodic coefficients . Applicable Analysis , 69 : 83 – 104 .
   Google Scholar
• Kordonis , I.-G.E. , Philos , Ch.G. and Purnaras , I.K. 2004 . On the behavior of solutions of linear neutral integrodifferential equations with unbounded delay . Georgian Mathematical Journal , 11 : 337 – 348 .
   Google Scholar
• Ladas , G. 1991 . “ Recent developments in the oscillation of delay difference equations ” . In Lecture Notes in Pure and Appl. Math. , Vol. 127 , 321 – 332 . New York : Dekker . Differential Equations (Colorado Springs, CO, 1989)
   Google Scholar
• Ladas , G. , Pakula , L. and Wang , Z. 1992 . Necessary and sufficient conditions for the oscillation of difference equations . PanAmerican Mathematical Journal , 2 : 17 – 26 .
   Google Scholar
• Lakshmikantham , V. and Trigiante , D. 1998 . Theory of Difference Equations: Numerical Methods and Applications , New York : Academic Press, Inc. .
   Google Scholar
• Mickens , R. 1990 . Difference Equations , New York : Van Nostrand Reinhold .
   Google Scholar
• Norris, M.J., 1967, Unpublished notes on the delay differential equation x′(t)=bx(t − 1) where − 1/e ≤ b < 0, October.
   Google Scholar
• Philos , Ch.G. 1998 . Asymptotic behaviour, nonoscillation and stability in periodic first-order linear delay differential equations . Proceedings of the Royal Society of Edinburgh: Section A , 128 : 1371 – 1387 .
   Google Scholar
• Philos , Ch.G. and Purnaras , I.K. 2001 . Periodic first order linear neutral delay differential equations . Applied Mathematics and Computation , 117 : 203 – 222 .
   Web of Science ®Google Scholar
• Philos , Ch.G. and Purnaras , I.K. 2004 . The behavior of solutions of linear Volterra difference equations with infinite delay . Computers & Mathematics with Applications , 47 : 1555 – 1563 .
   Web of Science ®Google Scholar
• Philos , Ch.G. and Purnaras , I.K. 2004 . Asymptotic properties, nonoscillation, and stability for scalar first order linear autonomous neutral delay differential equations . Electronic Journal of Differential Equations , 2004 ( 03 ) : 1 – 17 .
   Google Scholar
• Philos , Ch.G. and Purnaras , I.K. 2004 . An asymptotic result for some delay difference equations with continuous variable . Advances in Difference Equations , 2004 ( 1 ) : 1 – 10 .
   Google Scholar
• Philos , Ch.G. and Purnaras , I.K. 2004 . An asymptotic result and a stability criterion for linear nonautonomous delay difference equations . Archives of Mathematics (Basel) , 83 : 243 – 255 .
   Web of Science ®Google Scholar
• Philos , Ch.G. and Purnaras , I.K. 2004 . On the behavior of the solutions for certain linear autonomous difference equations . Journal of Difference Equations and Applications , 10 : 1049 – 1067 .
   Web of Science ®Google Scholar
• Philos , Ch.G. and Purnaras , I.K. 2005 . The behavior of the solutions of periodic linear neutral delay difference equations . Journal of Computational and Applied Mathematics , 175 : 209 – 230 .
   Web of Science ®Google Scholar
• Philos, Ch.G. and Purnaras, I.K., On the behavior of the solutions for certain first order linear autonomous functional differential equations. Rocky Mountain Journal of Mathematics, in press.
   Google Scholar
• Philos, Ch.G. and Purnaras, I.K., 2006, A result on the behavior of the solutions for scalar first order linear autonomous neutral delay differential equations. Mathematical Proceedings of the Cambridge Philosophical Society, 140, 349–358.
   Google Scholar
• Philos , Ch.G. and Purnaras , I.K. 2005 . Asymptotic behaviour and stability to linear non-autonomous neutral delay difference equations . Journal of Difference Equations and Applications , 11 : 503 – 513 .
   Web of Science ®Google Scholar
• Philos , Ch.G. and Purnaras , I.K. 2005 . More on the behavior of solutions to linear integrodifferential equations with unbounded delay . Funkcialaj Ekvacioj , 48 : 393 – 414 .
   Web of Science ®Google Scholar
• Philos, Ch.G. and Purnaras, I.K., 2006, On linear Volterra difference equations with infinite delay. Advances in Difference Equations, 2006, 1–28.
   Google Scholar
• Philos, Ch.G. and Purnaras, I.K., On the behavior of the solutions to periodic linear delay differential and difference equations. Journal of Mathematical Analysis and Applications, in press.
   Google Scholar
• Philos, Ch.G. and Purnaras, I.K., On periodic linear neutral delay differential and difference equations, submitted.
   Google Scholar
• Philos, Ch.G. and Purnaras, I.K., On the behavior of the solutions to autonomous linear difference equations with continuous variable, submitted.
   Google Scholar
• Pituk , M. 2001 . The limits of the solutions of a nonautonomous linear delay difference equation . Computers & Mathematics with Applications , 42 : 543 – 550 .
   Web of Science ®Google Scholar
• Pituk , M. 2002 . Asymptotic behavior of a nonhomogeneous linear recurrence system . Journal of Mathematical Analysis and Applications , 267 : 626 – 642 .
   Web of Science ®Google Scholar
• Pituk , M. 2005 . Cesàro summability in a linear autonomous difference equation . Proceedings of the American Mathematical Society , 133 : 3333 – 3339 .
   Web of Science ®Google Scholar
• Sharkovsky , A.N. , Maistrenko , Yu.L. and Romanenko , E.Yu. 1993 . Difference Equations and Their Applications , Dordrecht : Kluwer Academic Publishers .
   Google Scholar
• Shen , J.H. 2000 . Comparison and oscillation results for difference equations with continuous variable . Indian Journal of Pure and Applied Mathematics , 31 : 1633 – 1642 .
   Web of Science ®Google Scholar
• Yan , J. and Zhang , F. 1999 . Oscillation for system of delay difference equations . Journal of Mathematical Analysis and Applications , 230 : 223 – 231 .
   Web of Science ®Google Scholar
• Zhang , Y. , Yan , J. and Zhao , A. 1997 . Oscillation criteria for a difference equation . Indian Journal of Pure and Applied Mathematics , 28 : 1241 – 1249 .
   Web of Science ®Google Scholar