Geodesic
Oscillation and nonoscillation of higher order self-adjoint differential equations
Czechoslovak Mathematical Journal, Tome 52 (2002) no. 4, pp. 833-849 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

Oscillation and nonoscillation criteria for the higher order self-adjoint differential equation \[ (-1)^n(t^{\alpha }y^{(n)})^{(n)}+q(t)y=0 \qquad \mathrm{(*)}\] are established. In these criteria, equation $(*)$ is viewed as a perturbation of the conditionally oscillatory equation \[ (-1)^n(t^{\alpha }y^{(n)})^{(n)}- \frac{\mu _{n,\alpha }}{t^{2n-\alpha }}y=0, \] where $\mu _{n,\alpha }$ is the critical constant in conditional oscillation. Some open problems in the theory of conditionally oscillatory, even order, self-adjoint equations are also discussed.
Oscillation and nonoscillation criteria for the higher order self-adjoint differential equation \[ (-1)^n(t^{\alpha }y^{(n)})^{(n)}+q(t)y=0 \qquad \mathrm{(*)}\] are established. In these criteria, equation $(*)$ is viewed as a perturbation of the conditionally oscillatory equation \[ (-1)^n(t^{\alpha }y^{(n)})^{(n)}- \frac{\mu _{n,\alpha }}{t^{2n-\alpha }}y=0, \] where $\mu _{n,\alpha }$ is the critical constant in conditional oscillation. Some open problems in the theory of conditionally oscillatory, even order, self-adjoint equations are also discussed.
Classification : 34B05, 34C10
Keywords: self-adjoint differential equation; oscillation and nonoscillation criteria; variational method; conditional oscillation 
@article{CMJ_2002_52_4_a14,
     author = {Do\v{s}l\'y, Ond\v{r}ej and Osi\v{c}ka, Jan},
     title = {Oscillation and nonoscillation of higher order self-adjoint differential equations},
     journal = {Czechoslovak Mathematical Journal},
     pages = {833--849},
     year = {2002},
     volume = {52},
     number = {4},
     mrnumber = {1940063},
     zbl = {1023.34028},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2002_52_4_a14/}
}
TY  - JOUR
AU  - Došlý, Ondřej
AU  - Osička, Jan
TI  - Oscillation and nonoscillation of higher order self-adjoint differential equations
JO  - Czechoslovak Mathematical Journal
PY  - 2002
SP  - 833
EP  - 849
VL  - 52
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/CMJ_2002_52_4_a14/
LA  - en
ID  - CMJ_2002_52_4_a14
ER  - 
%0 Journal Article
%A Došlý, Ondřej
%A Osička, Jan
%T Oscillation and nonoscillation of higher order self-adjoint differential equations
%J Czechoslovak Mathematical Journal
%D 2002
%P 833-849
%V 52
%N 4
%U http://geodesic.mathdoc.fr/item/CMJ_2002_52_4_a14/
%G en
%F CMJ_2002_52_4_a14
Došlý, Ondřej; Osička, Jan. Oscillation and nonoscillation of higher order self-adjoint differential equations. Czechoslovak Mathematical Journal, Tome 52 (2002) no. 4, pp. 833-849. http://geodesic.mathdoc.fr/item/CMJ_2002_52_4_a14/