A two-parameter boundary problem for second order differential system

1979 ◽  
Vol 120 (1) ◽  
pp. 293-303
Author(s):  
G. J. Etgen ◽  
S. C. Tefteller
Keyword(s):  
Boundary Problem ◽  
Differential System ◽  
Second Order ◽  
Two Parameter

An Asymptotical Stability in Variational Sense for Second Order Systems

2010 ◽  
Vol 10 (1) ◽  
Author(s):  
Dariusz Idczak ◽  
Stanisław Walczak
Keyword(s):  
Sobolev Space ◽  
Differential System ◽  
Sufficient Conditions ◽  
Zero Solution ◽  
Second Order ◽  
Functional Parameter ◽  
Asymptotical Stability ◽  
Parameter Control ◽  
Initial Condition ◽  
Second Order Systems

AbstractIn this paper, a new, variational concept of asymptotical stability of zero solution to an ordinary differential system of the second order, considered in Sobolev space, is presented. Sufficient conditions for an asymptotical stability in a variational sense with respect to initial condition and functional parameter (control) are given. Relation to the classical asymptotical stability is illustrated.

scholarly journals Second Approximate Solution of Duffing Equation with Strong Nonlinearity by Homotopy Perturbation Method

1970 ◽  
Vol 30 ◽  
pp. 59-75
Author(s):  
M Alhaz Uddin ◽  
M Abdus Sattar
Keyword(s):  
Approximate Solution ◽  
Nonlinear Systems ◽  
Perturbation Method ◽  
Differential System ◽  
Homotopy Perturbation Method ◽  
Approximate Solutions ◽  
Second Order ◽  
Strong Nonlinearity ◽  
Analytical Technique ◽  
Homotopy Perturbation

 In this paper, the second order approximate solution of a general second order nonlinear ordinary differential system, modeling damped oscillatory process is considered. The new analytical technique based on the work of He’s homotopy perturbation method is developed to find the periodic solution of a second order ordinary nonlinear differential system with damping effects. Usually the second or higher order approximate solutions are able to give better results than the first order approximate solutions. The results show that the analytical approximate solutions obtained by homotopy perturbation method are uniformly valid on the whole solutions domain and they are suitable not only for strongly nonlinear systems, but also for weakly nonlinear systems. Another advantage of this new analytical technique is that it also works for strongly damped, weakly damped and undamped systems. Figures are provided to show the comparison between the analytical and the numerical solutions. Keywords: Homotopy perturbation method; damped oscillation; nonlinear equation; strong nonlinearity. GANIT J. Bangladesh Math. Soc. (ISSN 1606-3694) 30 (2010) 59-75  DOI: http://dx.doi.org/10.3329/ganit.v30i0.8504

scholarly journals ON THE INTEGRABILITY OF A CLASS OF MONGE–AMPÈRE EQUATIONS

2001 ◽  
Vol 13 (04) ◽  
pp. 529-543 ◽  
Author(s):  
J. C. BRUNELLI ◽  
M. GÜRSES ◽  
K. ZHELTUKHIN
Keyword(s):  
Sigma Models ◽  
Minimal Surfaces ◽  
Second Order ◽  
Lax Representation ◽  
Parameter Equation ◽  
Monge Ampere ◽  
Two Parameter

We give the Lax representations for the elliptic, hyperbolic and homogeneous second order Monge–Ampère equations. The connection between these equations and the equations of hydrodynamical type give us a scalar dispersionless Lax representation. A matrix dispersive Lax representation follows from the correspondence between sigma models, a two parameter equation for minimal surfaces and Monge–Ampère equations. Local as well nonlocal conserved densities are obtained.

scholarly journals Periodic in distribution solution for a telegraph equation

1999 ◽  
Vol 12 (2) ◽  
pp. 121-131 ◽  
Author(s):  
A. Ya. Dorogovtsev
Keyword(s):  
Boundary Problem ◽  
Stochastic Equation ◽  
Existence Of Solutions ◽  
Random Processes ◽  
Telegraph Equation ◽  
Second Order ◽  
Distribution Solution ◽  
Stochastic Boundary

In this paper we study an abstract stochastic equation of second order and stochastic boundary problem for the telegraph equation in a strip. We prove the existence of solutions, which are d-periodic (periodic in distribution) random processes.

Sign in / Sign up

Export Citation Format

Share Document