| Title:
|
The impact of unbounded swings of the forcing term on the asymptotic behavior of functional equations (English) |
| Author:
|
Singh, Bhagat |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
50 |
| Issue:
|
1 |
| Year:
|
2000 |
| Pages:
|
15-24 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Necessary and sufficient conditions have been found to force all solutions of the equation \[ (r(t)y^{\prime }(t))^{(n-1)} + a(t)h(y(g(t))) = f(t), \] to behave in peculiar ways. These results are then extended to the elliptic equation \[ |x|^{p-1} \Delta y(|x|) + a(|x|)h(y(g(|x|))) = f(|x|) \] where $ \Delta $ is the Laplace operator and $p \ge 3$ is an integer. (English) |
| Keyword:
|
oscillatory |
| Keyword:
|
nonoscillatory |
| Keyword:
|
exterior domain |
| Keyword:
|
elliptic |
| Keyword:
|
functional equation |
| MSC:
|
34K11 |
| MSC:
|
34K25 |
| MSC:
|
35B40 |
| MSC:
|
35J60 |
| MSC:
|
35R10 |
| idZBL:
|
Zbl 1045.34051 |
| idMR:
|
MR1745454 |
| . |
| Date available:
|
2009-09-24T10:29:20Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127543 |
| . |
| Reference:
|
[1] L. S. Chen: On the oscillation and asymptotic properties for general nonlinear differential equations.Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 51 (1976), 211–216. MR 0481263 |
| Reference:
|
[2] J. R. Graef: Oscillation, nonoscillation and growth of solutions of nonlinear functional differential equations of arbitrary order.J. Math. Anal. Appl. 60 (1977), 398-409. Zbl 0377.34023, MR 0454249, 10.1016/0022-247X(77)90029-4 |
| Reference:
|
[3] M. E. Hammett: Nonoscillation properties of a nonlinear differential equation.Proc. Amer. Math. Soc. 30 (1971), 92–96. Zbl 0215.15001, MR 0279384, 10.1090/S0002-9939-1971-0279384-5 |
| Reference:
|
[4] T. Kusano and H. Onose: Asymptotic behavior of nonoscillatory solutions of second order functional equations.Bull. Austral. Math. Soc. 13 (1975), 291–299. MR 0397114, 10.1017/S0004972700024473 |
| Reference:
|
[5] T. Kusano and H. Onose: Nonoscillation theorems for differential equations with deviating argument.Pacific J. Math. 62 (1976), 185–192. MR 0417536 |
| Reference:
|
[6] B. Singh and R. S. Dahiya: Existence of slow oscillations in functional equations.J. Math. Anal. Appl. 48 (1990), 213–222. MR 1052056, 10.1016/0022-247X(90)90039-I |
| Reference:
|
[7] B. Singh and R. S. Dahiya: On oscillation of second order retarded equations.J. Math. Anal. Appl. 47 (1974), 504–512. MR 0355269, 10.1016/0022-247X(74)90003-1 |
| Reference:
|
[8] B. Singh: Asymptotically vanishing oscillatory trajectories in second order retarded equations.SIAM J. Math. Anal. 7 (1976), 37–44. Zbl 0321.34058, MR 0425308, 10.1137/0507005 |
| Reference:
|
[9] B. Singh: A correction to “Forced oscillations in general ordinary differential equations with deviating arguments”.Hiroshima Math. J. 9 (1979), 277–302. Zbl 0409.34070, MR 0529336, 10.32917/hmj/1206135207 |
| Reference:
|
[10] B. Singh: Nonoscillation of forced fourth order retarded equations.SIAM J. Appl. Math. 28 (1975), 265–269. MR 0361376, 10.1137/0128021 |
| Reference:
|
[11] B. Singh: Asymptotic nature of nonoscillatory solutions of $n$th order retarded differential equations.SIAM J. Math. Anal. 6 (1975), 784–795. Zbl 0314.34082, MR 0430474, 10.1137/0506069 |
| Reference:
|
[12] B. Singh: General functional differential equations and their asymptotic oscillatory behavior.Yokohama Math. J. 24 (1976), 125–132. Zbl 0361.34062, MR 0425309 |
| Reference:
|
[13] B. Singh: Forced oscillations in general ordinary differential equations with deviating arguments.Hiroshima Math. J. 6 (1976), 7–14. Zbl 0329.34057, MR 0402233, 10.32917/hmj/1206136446 |
| Reference:
|
[14] B. Singh: Necessary and sufficient conditions for eventual decay of oscillations in general functional equations with delays.Hiroshima Math. J. 10 (1980), 1–9. MR 0558845, 10.32917/hmj/1206134574 |
| Reference:
|
[15] B. Singh: On the oscillation of a Volterra integral equation.Czechoslovak Math. J. 45 (1995), 699–707. Zbl 0847.45003, MR 1354927 |
| Reference:
|
[16] B. Singh: Necessary and sufficient conditions for eventually vanishing oscillatory solutions of functional equations with small delays.Internat. J. Math. & Math. Sci. 1 (1978), 269–283. Zbl 0389.34048, MR 0510559, 10.1155/S0161171278000307 |
| . |
