Geodesic
Asymptotic properties of solutions of second order quasilinear functional differential equations of neutral type
Mathematica Bohemica, Tome 125 (2000) no. 2, pp. 199-213

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

MR Zbl
This paper establishes existence of nonoscillatory solutions with specific asymptotic behaviors of second order quasilinear functional differential equations of neutral type. Then sufficient, sufficient and necessary conditions are proved under which every solution of the equation is either oscillatory or tends to zero as $ t \to\infty$.
This paper establishes existence of nonoscillatory solutions with specific asymptotic behaviors of second order quasilinear functional differential equations of neutral type. Then sufficient, sufficient and necessary conditions are proved under which every solution of the equation is either oscillatory or tends to zero as $ t \to\infty$.
DOI : 10.21136/MB.2000.125952
Classification : 34K11, 34K25, 34K40
Keywords: quasilinear differential equations of neutral type; oscillatory; nonoscillatory solutions; Schauder-Tychonoff fixed-point theorem 
Kusano, Takaŝi; Marušiak, Pavol. Asymptotic properties of solutions of second order quasilinear functional differential equations of neutral type. Mathematica Bohemica, Tome 125 (2000) no. 2, pp. 199-213. doi: 10.21136/MB.2000.125952
@article{10_21136_MB_2000_125952,
     author = {Kusano, Taka\^{s}i and Maru\v{s}iak, Pavol},
     title = {Asymptotic properties of solutions of second order quasilinear functional differential equations of neutral type},
     journal = {Mathematica Bohemica},
     pages = {199--213},
     year = {2000},
     volume = {125},
     number = {2},
     doi = {10.21136/MB.2000.125952},
     mrnumber = {1768808},
     zbl = {0973.34067},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/MB.2000.125952/}
}
TY  - JOUR
AU  - Kusano, Takaŝi
AU  - Marušiak, Pavol
TI  - Asymptotic properties of solutions of second order quasilinear functional differential equations of neutral type
JO  - Mathematica Bohemica
PY  - 2000
SP  - 199
EP  - 213
VL  - 125
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.21136/MB.2000.125952/
DO  - 10.21136/MB.2000.125952
LA  - en
ID  - 10_21136_MB_2000_125952
ER  - 
%0 Journal Article
%A Kusano, Takaŝi
%A Marušiak, Pavol
%T Asymptotic properties of solutions of second order quasilinear functional differential equations of neutral type
%J Mathematica Bohemica
%D 2000
%P 199-213
%V 125
%N 2
%U http://geodesic.mathdoc.fr/articles/10.21136/MB.2000.125952/
%R 10.21136/MB.2000.125952
%G en
%F 10_21136_MB_2000_125952

[1] Elbert Á.: A half-linear second-order differential equation. Colloquiua Math. Soc. Janos Bolyai 30. Qualitative Theory of Differential Equations, Vol. I (Colloquium held in Szeged, August 1979). North-Holland, Amsterdam, 198J, pp. 153-180. | MR

[2] Elbert Á., Kusano T: Oscillation aud nonoscillation theorems for a class of second order quasilinear differential equations. Acta Math. Hungar. 56 (1990), 325-336. | DOI | MR

[3] Erbe L. E., Kong Q., Zhang B. G.: Oscillation Theory of Functional Differential Equations. Marcel Dekker Inc., New York, 1995. | MR

[4] Györi I., Ladas G.: Oscillation Theory of Delay Differential Equations. Clarendon Press, Oxford, 1991. | MR

[5] Ivanov A.F., Kusano T.: Oscillation of solutions of second order nonlinear functional differential equations of neutral type. Ukrain. Math. J. 42 (1991), 1672-1683. | MR | Zbl

[6] Jaroš J., Kusano T., Marušiak P.: Oscillation and nonoscilìation theorems for second order quasilinear functional differential equations of neutral type. Adv. Math. Sci. Appl. To appear. | MR

[7] Jaroš J., Kusano T.: Asymptotic behavior of nonoscillatory solutions of nonlinear functional differential equations of neutral type. Funkcial. Ekvac. 32 (1989), 251-263. | MR

[8] Kitano M., Kusano T.: On a class of second order quasìlinear ordinary differential equation. Hiroshima Math. J. 25 (1995), 321-335. | DOI | MR

[9] Kusano T., Naito Y.: Oscilłation and nonosciliation criteria for second order quasilinear differential equations. Acta Math. Hungar. 76 (1997), 55-73. | DOI | MR

[10] Kusano T., Naito Y., Ogata A.: Strong oscillation and nonoscillation of quasilinear differential equations of second order. Differential Equations Dynam. Systems 2 (1994), 1-10. | MR | Zbl

[11] Kusano T., Ogata A.: Existence and asymptotic behavior of positive solutions of second order quasilinear differential equations. Funkcial. Ekvac. 57 (1994), 345-361. | MR | Zbl

[12] Kusano T., Ogata A., Usami H.: Oscillation theory for a ciass of second order quasilinear ordinary differential equations with application to partial differential equations. Japan. J. Math. 19 (1993), 131-147. | DOI | MR

[13] Kusano T., Lalli B. S.: On osciilation of Һalf-linear differential equations with deviating arguments. Hiroshima Math. J. 2Jt (1994), 549-563. | MR

[14] Kusano T., Yoshida N.: Nonoscillation theorems for a class of quasilinear differential equations of second order. J. Math. Anal. Appl. 189 (1995), 127-155. | MR | Zbl

[15] Kusano T., Wang J.: Oscillation properties of half-linear functional differential quations of second order. Hiroshima Math. J. 25 (1995), 371-385. | DOI | MR

[16] Marušiak P.: Asymptotic properties of nonoscillatory solutions of neutral delay differential equations of n-th order. Czechoslovak Math. J. 47 (1997), 327-336. | DOI | MR

[17] Mirzov J. D.: On some analogs of Sturm's and Kneser's theorems for nonlinear systems. J. Math. Anal. Appl. 53(1976), 418-425. | DOI | MR | Zbl

[18] Naito Y.: Nonoscillatory solutions of neutral differential equations. Hiroshima Math. J. 29 (1990), 231-258. | DOI | MR | Zbl

[19] Wang. J.: Oscillation and nonoscillation for a class of second order quasilinear functional differential equations. Hiroshima Math. J. 27 (1997). | MR

[20] Wong P. J. Y., Agarwal R. P.: Oscillatory behavior of solutions of certain second order nonlinear differential equations. J. Math. Appl. 198 (1996), 337-354. | MR

Cité par Sources :