On the oscillatory integration of some ordinary differential equations

Octavian G. Mustafa

Address: Corresponding address: Str. Tudor Vladimirescu, Nr. 26 200534 Craiova, Dolj, Romania Faculty of Mathematics, D.A.L. University of Craiova, Romania

E-mail: octaviangenghiz@yahoo.com

Abstract: Conditions are given for a class of nonlinear ordinary differential equations $x^{\prime \prime }+a(t)w(x)=0$, $t\ge t_0\ge 1$, which includes the linear equation to possess solutions $x(t)$ with prescribed oblique asymptote that have an oscillatory pseudo-wronskian $x^{\prime }(t)-\frac{x(t)}{t}$.

AMSclassification: Primary: 34A30; Secondary: 34E05, 34K25.

Keywords: ordinary differential equation, asymptotic integration, prescribed asymptote, non-oscillation of solutions