Oscillation and nonoscillation of higher order self-adjoint differential equations

Ondřej Došlý; Jan Osička

Czechoslovak Mathematical Journal (2002)

  • Volume: 52, Issue: 4, page 833-849
  • ISSN: 0011-4642

Abstract

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Oscillation and nonoscillation criteria for the higher order self-adjoint differential equation ( - 1 ) n ( t α y ( n ) ) ( n ) + q ( t ) y = 0 ( * ) are established. In these criteria, equation ( * ) is viewed as a perturbation of the conditionally oscillatory equation ( - 1 ) n ( t α y ( n ) ) ( n ) - μ n , α t 2 n - α y = 0 , where μ n , α is the critical constant in conditional oscillation. Some open problems in the theory of conditionally oscillatory, even order, self-adjoint equations are also discussed.

How to cite

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Došlý, Ondřej, and Osička, Jan. "Oscillation and nonoscillation of higher order self-adjoint differential equations." Czechoslovak Mathematical Journal 52.4 (2002): 833-849. <http://eudml.org/doc/30748>.

@article{Došlý2002,
abstract = {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.},
author = {Došlý, Ondřej, Osička, Jan},
journal = {Czechoslovak Mathematical Journal},
keywords = {self-adjoint differential equation; oscillation and nonoscillation criteria; variational method; conditional oscillation; selfadjoint differential equation; oscillation and nonoscillation criteria; variational method; conditional oscillation},
language = {eng},
number = {4},
pages = {833-849},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Oscillation and nonoscillation of higher order self-adjoint differential equations},
url = {http://eudml.org/doc/30748},
volume = {52},
year = {2002},
}

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
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 52
IS - 4
SP - 833
EP - 849
AB - 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.
LA - eng
KW - self-adjoint differential equation; oscillation and nonoscillation criteria; variational method; conditional oscillation; selfadjoint differential equation; oscillation and nonoscillation criteria; variational method; conditional oscillation
UR - http://eudml.org/doc/30748
ER -

References

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