On the asymptotic behavior at infinity of solutions to quasi-linear differential equations

Title:

On the asymptotic behavior at infinity of solutions to quasi-linear differential equations

Creator:

Astashova, Irina

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:07df2abe-82d8-4df4-89fe-26338f08339d
uuid:07df2abe-82d8-4df4-89fe-26338f08339d
doi:10.21136/MB.2010.140828

Subject:

quasi-linear ordinary differential equation of higher order, existence of non-oscillatory solution, and oscillatory solution

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

Sufficient conditions are formulated for existence of non-oscillatory solutions to the equation y (n) + ∑ n−1 j=0 aj (x)y (j) + p(x)|y| k sgn y = 0 with n > 1, real (not necessarily natural) k > 1, and continuous functions p(x) and aj (x) defined in a neighborhood of +∞. For this equation with positive potential p(x) a criterion is formulated for existence of non-oscillatory solutions with non-zero limit at infinity. In the case of even order, a criterion is obtained for all solutions of this equation at infinity to be oscillatory. Sufficient conditions are obtained for existence of solution to this equation which is equivalent to a polynomial.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

373-382

Source:

Mathematica bohemica | 2010 Volume:135 | Number:4

Harvested from:

CDK

Metadata only:

false