## Differential and Integral Equations

### Half-linear differential equations with oscillating coefficient

#### Abstract

We study asymptotic properties of solutions of the nonoscillatory half-linear differential equation $(a(t)\Phi(x^{\prime}))^{\prime}+b(t)\Phi(x)=0$ where the functions $a,b$ are continuous for $t\geq0,$ $a(t)>0$ and $\Phi(u)=|u|^{p-2}u$, $p>1$. In particular, the existence and uniqueness of the zero-convergent solutions and the limit characterization of principal solutions are proved when the function $b$ changes sign. An integral characterization of the principal solutions, the boundedness of all solutions, and applications to the Riccati equation are considered as well.

#### Article information

Source
Differential Integral Equations, Volume 18, Number 11 (2005), 1243-1256.

Dates
First available in Project Euclid: 21 December 2012

https://projecteuclid.org/euclid.die/1356059740

Mathematical Reviews number (MathSciNet)
MR2174819

Zentralblatt MATH identifier
1212.34144

Subjects
Primary: 34C11: Growth, boundedness
Secondary: 34B40: Boundary value problems on infinite intervals

#### Citation

Cecchi, Mariella; Došlá, Zuzana; Marini, Mauro. Half-linear differential equations with oscillating coefficient. Differential Integral Equations 18 (2005), no. 11, 1243--1256. https://projecteuclid.org/euclid.die/1356059740