Oscillation of nonlinear partial difference equations with delays

Computers and Mathematics with Applications

Volumn 32, Issue 12, 1996, Pages 29-39

  Shi, B ^a,b   Wang, Z C ^b   Yu, J S ^b  

^a HUNAN UNIVERSITY   (China)

^b NAVAL AERONAUTICAL AND ASTRONAUTICAL UNIVERSITY   (China)

Author keywords

Discrete Gaussian formula; Hyperbolic partial difference equations with delays; Neutral type; Oscillation; Parabolic partial difference equations with delays

Indexed keywords

ASYMPTOTIC STABILITY; DIFFERENTIAL EQUATIONS; NONLINEAR EQUATIONS; OSCILLATIONS; PARTIAL DIFFERENTIAL EQUATIONS;

DISCRETE GAUSSIAN FORMULA; LOGISTIC EQUATION; NEUTRAL TYPE; NONLINEAR PARTIAL DIFFERENCE EQUATIONS WITH DELAYS;

DIFFERENCE EQUATIONS;

EID: 0030378867     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0898-1221(96)00205-2     Document Type: Article

References (26)

1. B.T. Cui, Oscillation theorems of nonlinear parabolic equations of neutral type, Math. J. Toyama Univ., 14, 113-123 (1991).
2. B.T. Cui, Oscillation properties for parabolic equations of neutral type, Comment. Math. Univ. Carolinae 33, 581-588 (1992).
3. B.T. Cui, Oscillation theorems for nonlinear hyperbolic equations with deviating arguments, Acta Sci. Math. (Szeged) 58, 159-168 (1993).
4. B. Liu, Oscillation of solutions of nonlinear neutral partial differential equations, (in Chinese), Appl. Math. - A J. Chin. Univs., Ser. A 10 (3), 249-256 (1995).
5. D.P. Mishev, Oscillatory properties of the solutions of hyperbolic differential equations with "maximum", Hiroshima Math. J. 16, 77-83 (1986).
6. D.P. Mishev, Necessary and sufficient conditions for oscillation of neutral type parabolic differential equations, Comptes Kendus Acad. Bulg. Sci. 44 (3), 11-15 (1991).
7. D.P. Mishev, Oscillation of the solutions of neutral type hyperbolic differential equations, Math. Balkanica 5, 121-128 (1991).
8. D.P. Mishev and D.D. Bainov, Oscillation properties of the solutions of hyperbolic equations of neutral type, In Proc. of the Collog. on Qualitative Theory of Differential Eqns., pp. 771-780, Szeged, (1984).
9. D.P. Mishev and D.D. Bainov, Oscillation properties of the solutions of a class of hyperbolic equations of neutral type, Funkcial. Ekvac. 29, 213-218 (1986).
10. D.P. Mishev and D.D. Bainov, Oscillation of the solutions of parabolic differential equations of neutral type, Appl. Math. Comput. 28, 97-112 (1988).
11. J. Wiener and L. Debnath, Partial differential equations with piecewise constant delay, Internat. J. Math. & Math. Sci. 14, 485-496 (1991).
12. N. Yoshida, Oscillation of nonlinear parabolic equations with functional arguments, Hiroshima Math. J. 16, 305-314 (1986).
13. N. Yoshida, Forced oscillation of solutions of parabolic equations, Bull. Austral. Math. Soc. 36, 189-294 (1987).
14. N. Yoshida, On the zeros of solutions of nonlinear hyperbolic equations, In Proc. Roy. Soc. Edinburgh, Volume 106A, pp. 121-129, (1987).
15. N. Yoshida, On the zeros of solutions of hyperbolic equations of neutral type, Diff. Int. Eqns. 3, 155-160 (1990).
16. K. Gopalsamy and P.X. Weng, On the stability of a neutral integro-partial differential equation, Bull. Inst. Math. Acad. Sinica 20, 267-284 (1992).
17. S. Murakami, Asymptotic behavior in a class of integrodifferential equations with diffusion, Methods Appl. Anal. 2 (2), 237-247 (1995).
18. S. Murakami, Stable equilibrium point of some diffusive functional differential equations, Nonl. Anal., TMA 25, 1037-1043 (1995).
19. B. Shi, Z.C. Wang and J.S. Yu, Stability of parabolic Volterra integro-partial differential equations and their discrete analogues, Diff. Eqns. Dynam. Syst. (to appear).
20. S.S. Cheng, A sharp condition for the ground state of difference equations, Appl. Anal., 34, 105-109 (1989).
21. S.S. Cheng, L.Y. Hsieh and D.Z.T. Chao, Discrete Lyapunov inequality conditions for partial difference equations, Hiroshima Math. J., 19, 229-239 (1990).
22. B. Shi, Z.C. Wang and J.S. Yu, Square summable stability in parabolic Volterra difference equations, Methods Appl. Anal. (to appear).
23. B.G. Zhang, S.T. Liu and S.S. Cheng, Oscillation of a class of delay partial difference equations, J. Difference Eqns. and Appl. 1, 215-226 (1995).
24. W.G. Kelley and A.C. Peterson, Difference Equations: An Introduction with Applications, Acad. Press, (1991).
25. J.S. Yu and Z.C. Wang, Asymptotic behavior and oscillation in delay difference equations, Funkcial. Ekvac. 37, 241-248 (1994).
26. S.L. Xie, Stability of solutions of a class of parabolic partial functional differential equations with deviating arguments, (in Chinese), Chin. Sci. Bull. 36, 1435-1436 (1991).