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Keywords:
ordinary differential equation; asymptotic integration; prescribed asymptote; non-oscillation of solutions
ordinary differential equation; asymptotic integration; prescribed asymptote; non-oscillation of solutions
Summary:
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 $x^{\prime }(t)-\frac{x(t)}{t}$.
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