Geodesic
Counterexamples to a Conjecture for Neutral Equations
Canadian mathematical bulletin, Tome 36 (1993) no. 1, pp. 74-77

Voir la notice de l'article provenant de la source Cambridge University Press

A collection of examples of first order linear neutral differential delay equations having a nonoscillatory solution with lim sup = ∞ and lim inf = 0 at ∞ is given. This disproves a recent conjecture about the asymptotic behavior of solutions to such equations.
DOI : 10.4153/CMB-1993-011-0
Mots-clés : 34K15 
Krisztin, T.; Mathsen, R. M.; Yuantong, Xu. Counterexamples to a Conjecture for Neutral Equations. Canadian mathematical bulletin, Tome 36 (1993) no. 1, pp. 74-77. doi: 10.4153/CMB-1993-011-0
@article{10_4153_CMB_1993_011_0,
     author = {Krisztin, T. and Mathsen, R. M. and Yuantong, Xu},
     title = {Counterexamples to a {Conjecture} for {Neutral} {Equations}},
     journal = {Canadian mathematical bulletin},
     pages = {74--77},
     year = {1993},
     volume = {36},
     number = {1},
     doi = {10.4153/CMB-1993-011-0},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1993-011-0/}
}
TY  - JOUR
AU  - Krisztin, T.
AU  - Mathsen, R. M.
AU  - Yuantong, Xu
TI  - Counterexamples to a Conjecture for Neutral Equations
JO  - Canadian mathematical bulletin
PY  - 1993
SP  - 74
EP  - 77
VL  - 36
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1993-011-0/
DO  - 10.4153/CMB-1993-011-0
ID  - 10_4153_CMB_1993_011_0
ER  - 
%0 Journal Article
%A Krisztin, T.
%A Mathsen, R. M.
%A Yuantong, Xu
%T Counterexamples to a Conjecture for Neutral Equations
%J Canadian mathematical bulletin
%D 1993
%P 74-77
%V 36
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1993-011-0/
%R 10.4153/CMB-1993-011-0
%F 10_4153_CMB_1993_011_0

[1] 1. Anno, O. and Györi, I., Necessary and sufficient conditions for oscillation of a neutral differential system with several delays, J. Diff. Eqns. 81(1989), 98–105. Google Scholar

[2] 2. Farrell, K., Grove, E. A. and Ladas, G., Neutral delay differential equations with positive and negative coefficients, Appl Anal. 27(1988), 181–197. Google Scholar

[3] 3. Grammatikopoulos, M. K., Grove, E. A. and Ladas, G., Oscillation and asymptotic behavior of neutral differential equations with deviating arguments, Appl. Anal. 22(1986), 1–19. Google Scholar

[4] 4. Mathsen, R. M., Yuantong, Xu and Qiru, Wang, Asymptotics and oscillation for first order neutral functional differential equations, preprint. Google Scholar

[5] 5. Philos, Ch. G. and Sfleas, Y. G., On the nature of the nonoscillatory solutions of a class of neutral delay differential equations,]. Math. Anal. Appl. 154(1991),417–434. Google Scholar

[6] 6. Ruan, Shigui, Oscillations for first order neutral differential equations with variable coefficients, Austral. Math. Soc. 43(1991), 147–152. Google Scholar

[7] 7. Schultz, S. W., Necessary and sufficient conditions for oscillation of neutral equations with mixed arguments. In: Differential Equations and Applications, Proceedings of the Int. Conf. on the Theory and Appl. of Diff. Eqns., Columbus, Ohio, 1988, Ohio University Press, Athens, 1989. Google Scholar

Cité par Sources :