Differential and Integral Equations

Half-linear differential equations with oscillating coefficient

Mariella Cecchi, Zuzana Došlá, and Mauro Marini

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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

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

First available in Project Euclid: 21 December 2012

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


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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