Half-linear differential equations with oscillating coefficient. (English) Zbl 1212.34144

Cecchi, Mariella; Došlá, Zuzana; Marini, Mauro

Differ. Integral Equ. 18, No. 11, 1243-1256 (2005).

Summary: We study asymptotic properties of solutions of the nonoscillatory half-linear differential equation \[ (a(t)\Phi (x'))'+b(t)\Phi (x)=0, \] where the functions \(a,b\) are continuous for \(t\geq 0\), \(a(t)>0\) 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.

MSC:

34D05	Asymptotic properties of solutions to ordinary differential equations
34C11	Growth and boundedness of solutions to ordinary differential equations
34A34	Nonlinear ordinary differential equations and systems

Keywords:

Riccati equation