Differential and Integral Equations

Half-linear differential equations with oscillating coefficient

Mariella Cecchi, Zuzana Došlá, and Mauro Marini

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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

Permanent link to this document
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


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