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Asymptotic behaviour of oscillatory solutions of $n$ -th order differential equations with quasiderivatives

Miroslav Bartušek — 1997

Czechoslovak Mathematical Journal

Sufficient conditions are given under which the sequence of the absolute values of all local extremes of $y^{[i]}$ , $i \in {0, 1, \dots, n - 2}$ of solutions of a differential equation with quasiderivatives $y^{[n]} = f (t, y^{[0]}, \dots, y^{[n - 1]})$ is increasing and tends to $\infty$ . The existence of proper, oscillatory and unbounded solutions is proved.

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Asymptotic behaviour of oscillatory solutions of $n$ -th order differential equations with quasiderivatives

Note on the theory of dispersions of the differential equation $y^{''} = q (t) y$

Connection between asymptotic properties and zeros of solutions of $y^{''} = q (t) y$

On oscillatory solutions of nonlinear differential equations of the $n$ -th order vanishing at infinity

The asymptotic behaviour of oscillatory solutions of the equation of the fourth order

On zeros of solutions of the differential equation ${(p (t) y^{'})}^{'} + f (t, y, y^{'}) = 0$

On zeros of solutions of the differential equation $y^{''} + f (t, y) g (y^{'}) = 0$

On oscillatory solution of the differential equations of the $n$ -th order

On proper oscillatory solutions of the nonlinear differential equations of the $n$ -th order

On existence of oscillatory solution of the system of differential equations

On asymptotic properties and distribution of zeros of solutions of $y^{''} + f (t, y, y^{'}) = 0$

The asymptotic behaviour of solutions of the differential equation of the third order

On asymptotic properties of oscillatory solutions of the system of differential equations of fourth order

Monotonicity theorems concerning differential equations $y^{''} + f (t, y, y^{'}) = 0$

On distribution of zeros of solutions of the differential equation ${(p (t) y^{'})}^{'} + f (t, y, y^{'}) = 0$

Monotonicity theorems for second order non-linear differential equations

On the distribution of zeros of solutions of some types of differential equation $y^{''} = q (t) y$

On $L^{p}$ -solutions of the differential equation $y " = q (t) y$

On asymptotic behaviour of central dispersions of linear differential equations of the second order

On relations among dispersions of an oscillatory differential equation $y^{''} = q (t) y$