| Title | OSCILLATORY PROPERTIES OF SOLUTIONS OF n-TH ORDER DIFFERENTIAL EQUATIONS WITH DEVIATING ARGUMENTS DEPENDING ON THE UNKNOWN FUNCTION |
| Publication Type | Journal Article |
| Year of Publication | 2006 |
| Authors | Markova, NT, Simeonov, PS |
| Secondary Title | Communications in Applied Analysis |
| Volume | 10 |
| Issue | 4 |
| Start Page | 451 |
| Pagination | 467 |
| Date Published | 12/2006 |
| Type of Work | scientific: mathematics |
| ISSN | 1083–2564 |
| AMS | 34K15 |
| Abstract | In this paper differential equation of the type
is considered, where
|
| URL | http://www.acadsol.eu/en/articles/10/4/3.pdf |
| Short Title | Oscillatory Properties of Solutions |
| Refereed Designation | Refereed |
| Full Text | REFERENCES[1] S.R. Grace, Oscillation theorems for n-th order differential equations with deviating arguments, J. Math. Anal. Appl., 101 (1984), 268-296.
[2] S.R. Grace, Oscillatory properties of functional differential equations, J. Math. Anal. Appl., 160 (1991), 60-78. [3] S.R. Grace and B.S. Lalli, Oscillation theorems for n-th order delay differential equations, J. Math. Anal. Appl., 91 (1983), 352-366. [4] S.R. Grace and B.S. Lalli, Oscillatory and asymptotic behavior of solutions of differential equations with deviating arguments, J. Math. Anal. Appl., 104 (1984), 79-94. [5] S.R. Grace and B.S. Lalli, Oscillation of even order differential equations with deviating arguments, J. Math. Anal. Appl., 147 (1990), 569-579. [6] R.S. Dahiya and O. Akinyele, Oscillation theorems of n-th order functional differential equations with forcing terms, J. Math. Anal. Appl., 109 (1985), no. 2, 325-332. [7] I.T. Kiguradze, On the oscillation of solutions of the equation dmu/dtm + a(t)|u|n signu = 0, Mat. Sb., 65 (1964), no. 2, 172-187, In Russian. [8] Y. Kitamura, Oscillation of functional differential equations with general deviating argument, Hiroshima Math. J., 15 (1985), 445-491. [9] N.T. Markova and P.S. Simeonov, Asymptotic and oscillatory properties of the solutions of differential equations with delays depending on the unknown function, Invited lectures delivered at the VII-th Int. Colloquium on Differential Equations, Volume 2, August 18-23, 1996. Plovdiv, Bulgaria, 71-78. [10] N.T. Markova and P.S. Simeonov, On the asymptotic behaviour of the solutions of a class of differential equations of second order with delay depending on the unknown function, Invited lectures delivered at the VII-th Int. Colloquium on Differential Equations, August 18-23, 1996, Plovdiv, Bulgaria, Volume 1, 89-100. [11] N.T. Markova and P.S. Simeonov, Oscillation theorems for n-th order nonlinear differential equations with forcing terms and deviating arguments depending on the unknown function, Communications in Applied Analysis, 9 (2005),no. 3, 417-427. [12] N.T. Markova and P.S. Simeonov, Asymptotic and oscillatory behavior of n-th order forced differential equations with deviating argument depending on the unknown function, PanAmerican Mathematical Journal, 16 (2006), no. 1, 1-15. [13] Ch.G. Philos, Oscillatory and aymptotic behavior of all solutions of differential equations with deviating arguments, Proc. Roy. Soc. Edinburgh Sect. A, 81 (1978), 195-210. |
and the deviating arguments ∆j , j = 1, . . . , m depend on the independent variable t as well as on the unknown unction x. Sufficient conditions are found under which equation (E) is almost oscillatory.