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On the asymptotic behavior at infinity of solutions to quasi-linear differential equations

Irina Astashova (2010)

Mathematica Bohemica

Sufficient conditions are formulated for existence of non-oscillatory solutions to the equation $y^{(n)} + \sum_{j = 0}^{n - 1} a_{j} (x) y^{(j)} + p (x) {| y |}^{k} sgn y = 0$ with $n \geq 1$ , real (not necessarily natural) $k > 1$ , and continuous functions $p (x)$ and $a_{j} (x)$ defined in a neighborhood of $+ \infty$ . For this equation with positive potential $p (x)$ a criterion is formulated for existence of non-oscillatory solutions with non-zero limit at infinity. In the case of even order, a criterion is obtained for all solutions of this equation at infinity to be oscillatory. Sufficient conditions are obtained...

On the asymptotic behavior for a damped oscillator under a sublinear friction.

Jesús Ildefonso Díaz, Amable Liñán (2001)

RACSAM

Mostramos la existencia de dos curvas de datos iniciales (x0, v0) para las cuales las soluciones x(t) correspondientes del problema de Cauchy asociado a la ecuación xtt + |xt|α-1 xt + x = 0, supuesto α ∈ (0,1), se anulan idénticamente después de un tiempo finito. Mediante métodos asintóticos y argumentos de comparación mostramos que para muchos otros datos iniciales las soluciones decaen a 0, en un tiempo infinito, como t-α / (1-α).

Currently displaying 61 – 80 of 144

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Displaying 61 – 80 of 144

On the asymptotic behavior at infinity of solutions to quasi-linear differential equations

On the asymptotic behavior for a damped oscillator under a sublinear friction.

On the asymptotic behavior of solutions for a class of second order nonlinear differential equations.

On the asymptotic behavior of solutions of certain third-order nonlinear differential equations.

On the asymptotic behavior of solutions of nonlinear ordinary differential equations

On the asymptotic behavior of solutions of the second-order linear differential equation

On the asymptotic behavior of the one-sided Green's function for a differential operator near a singularity

On the asymptotic behaviour of solutions of certain ordinary differential equations

On the asymptotic behaviour of the equation $d z / d t = f (t, z)$ with a complex-valued function $f$

On the asymptotic classes of solutions of a superlinear differential equation

On the asymptotic integration of nonlinear dynamic equations.

On the asymptotic nature of a class of second order nonlinear systems.

On the asymptotic properties of solutions of nonlinear systems

On the asymptotic properties of solutions of nonlinear third order differential equation

On the asymptotic stability of solutions of functional-differential equations

On the asymptotic stability of two-dimensional linear systems

On the asymptotics of the real solutions to the general sixth Painlevé equation.

On the boundedness and oscillation of solutions to ${(m (t) x^{1})}^{1} + a (t) b (x) = 0$ .

On the boundedness and the stability results for the solutions of certain third order non-linear differential equations

On the convergence of a time-variant linear differential equation arising in identification

Currently displaying 61 – 80 of 144