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On some properties of the solution of the differential equation $u^{''} + \frac{2 u^{'}}{r} = u - u^{3}$

Valter Šeda, Ján Pekár (1990)

Aplikace matematiky

In the paper it is shown that each solution $u (r, α)$ ot the initial value problem (2), (3) has a finite limit for $r \to \infty$ , and an asymptotic formula for the nontrivial solution $u (r, α)$ tending to 0 is given. Further, the existence of such a solutions is established by examining the number of zeros of two different solutions $u (r, \bar{α})$ , $u (r, \hat{α})$ .

On some properties of third-order linear differential equation

Ján Regenda (1976)

Mathematica Slovaca

On some properties of trigonometric matrices

Ondřej Došlý (1987)

Časopis pro pěstování matematiky

On splitting solutions of a certain $n$ -th order differential equation

Vladimír Vlček (1985)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

On stability and instability of the roots of the oscillatory function in a certain nonlinear differential equation of the third order

Ján Andres (1986)

Časopis pro pěstování matematiky

On stability for time-periodic perturbations of harmonic oscillators

Min-Jei Huang (1989)

Annales de l'I.H.P. Physique théorique

On structure of solutions of a system of four differential inequalities.

Bartušek, Miroslav (1995)

Georgian Mathematical Journal

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 behaviour of solutions of the differential equations ${(r (t) y^{''})}^{'} + q (t) {(y^{'})}^{β} + p (t) y^{α} = f (t)$

N. Parhi, S. Parhi (1986)

Annales Polonici Mathematici

Currently displaying 101 – 120 of 323

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Displaying 101 – 120 of 323

On some properties of the solution of the differential equation $u^{''} + \frac{2 u^{'}}{r} = u - u^{3}$

On some properties of third-order linear differential equation

On some properties of trigonometric matrices

On splitting solutions of a certain $n$ -th order differential equation

On stability and instability of the roots of the oscillatory function in a certain nonlinear differential equation of the third order

On stability for time-periodic perturbations of harmonic oscillators

On structure of solutions of a system of four differential inequalities.

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

On the asymptotic behavior of solutions of the equation y" + p(x)y = 0

On the asymptotic classes of solutions of a superlinear differential equation

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

On the Asymptotic Relationship at Infinity between the solutions of two Differential Systems

On the basic central dispersion of the differential equation $y^{''} = q (t) y$ with an almost periodic coefficient

On the basic second kind central dispersion of $y^{'} = q (t) y$ with an almost periodic coefficient $q$

On the behaviour of solutions of the differential equations ${(r (t) y^{''})}^{'} + q (t) {(y^{'})}^{β} + p (t) y^{α} = f (t)$

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

On the boundedness of a solution of a system of non-linear differential equations

On the boundedness of solutions of a certain fourth-order nonlinear differential equation

On the Branching of Solutions of Quadratic Differential Equations.

On the bundle of solutions of a nonhomogeneous second order linear differential equation

Currently displaying 101 – 120 of 323