Asymptotic behavior of intermediate solutions of fourth-order nonlinear differential equations with regularly varying coefficients
We study the fourth-order nonlinear differential equation $$ \big(p(t)|x''(t)|^{\alpha-1} x''(t)\big)''+q(t)|x(t)|^{\beta-1}x(t)=0,\quad \alpha>\beta, $$ with regularly varying coefficient $p,q$ satisfying $$ \int_a^\infty t\Big(\frac{t}{p(t)}\Big)^{1/\alpha}\...
| 出版年: | Electronic Journal of Differential Equations |
|---|---|
| 主要な著者: | , |
| フォーマット: | 論文 |
| 言語: | 英語 |
| 出版事項: |
Texas State University
2016-06-01
|
| 主題: | |
| オンライン･アクセス: | http://ejde.math.txstate.edu/Volumes/2016/129/abstr.html |
| 要約: | We study the fourth-order nonlinear differential equation
$$
\big(p(t)|x''(t)|^{\alpha-1} x''(t)\big)''+q(t)|x(t)|^{\beta-1}x(t)=0,\quad
\alpha>\beta,
$$
with regularly varying coefficient $p,q$ satisfying
$$
\int_a^\infty t\Big(\frac{t}{p(t)}\Big)^{1/\alpha}\,dt<\infty.
$$
in the framework of regular variation. It is shown that complete information
can be acquired about the existence of all possible intermediate regularly
varying solutions and their accurate asymptotic behavior at infinity. |
|---|---|
| ISSN: | 1072-6691 |