Asymptotic behavior of solutions of a $2n^{th}$ order nonlinear differential equation

Title:

Asymptotic behavior of solutions of a $2n^{th}$ order nonlinear differential equation

Creator:

Lin, C. S.

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:15857afd-79e7-4a44-b783-03d8483b4c38
uuid:15857afd-79e7-4a44-b783-03d8483b4c38

Subject:

asymptotic behavior and higher order differential equation

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

In this paper we prove two results. The first is an extension of the result of G. D. Jones [4]: (A) Every nontrivial solution for \[ \left\rbrace \begin{array}{ll}(-1)^n u^{(2n)} + f(t,u) = 0,\hspace{5.0pt}\text{in} \hspace{5.0pt}(\alpha , \infty ), u^{(i)}(\xi ) = 0, \quad i = 0,1,\dots , n-1, \hspace{5.0pt} \text{and} \hspace{5.0pt}\xi \in (\alpha , \infty ), \end{array}\right.\] must be unbounded, provided $f(t,z)z\ge 0$, in $E \times \mathbb R$ and for every bounded subset $I$, $f(t,z)$ is bounded in $E \times I$. (B) Every bounded solution for $(-1)^n u^{(2n)} + f(t,u) = 0$, in $\mathbb R$, must be constant, provided $f(t,z)z\ge 0$ in $\mathbb R \times \mathbb R$ and for every bounded subset $I$, $f(t,z)$ is bounded in $\mathbb R \times I$.

Language:

English

Rights:

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

Coverage:

665-672

Source:

Czechoslovak Mathematical Journal | 2002 Volume:52 | Number:3

Harvested from:

CDK

Metadata only:

false