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.
Citation
Mariella Cecchi. Zuzana Došlá. Mauro Marini. "Half-linear differential equations with oscillating coefficient." Differential Integral Equations 18 (11) 1243 - 1256, 2005. https://doi.org/10.57262/die/1356059740
Information