Asymptotic splitting of systems of differential equations of second order with slowly varying and oscillating coefficients

1989 ◽  
Vol 40 (5) ◽  
pp. 548-550
Author(s):  
N. G. Kuz'ma
Keyword(s):  
Differential Equations ◽  
Second Order ◽  
Systems Of Differential Equations ◽  
Oscillating Coefficients ◽  
Asymptotic Splitting

scholarly journals Existence results for differential equations with reflection of the argument

1994 ◽  
Vol 57 (2) ◽  
pp. 237-260 ◽  
Author(s):  
Donal O'Regan
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Existence Results ◽  
Second Order ◽  
Systems Of Differential Equations ◽  
Nonlinear Alternative ◽  
Point Analysis ◽  
Second Order Equations

AbstractExistence principles are given for systems of differential equations with reflection of the argument. These are derived using fixed point analysis, specifically the Nonlinear Alternative. Then existence results are deduced for certain classes of first and second order equations with reflection of the argument.

scholarly journals APPLICATIONS OF LIE SYSTEMS IN DISSIPATIVE MILNE–PINNEY EQUATIONS

2009 ◽  
Vol 06 (04) ◽  
pp. 683-699 ◽  
Author(s):  
JOSÉ F. CARIÑENA ◽  
JAVIER DE LUCAS
Keyword(s):  
General Solution ◽  
Differential Equations ◽  
Geometric Approach ◽  
Second Order ◽  
Linear Differential Equations ◽  
Order Linear ◽  
Particular Solutions ◽  
Systems Of Differential Equations ◽  
Lie Systems ◽  
Linear Differential

We use the geometric approach to the theory of Lie systems of differential equations in order to study dissipative Ermakov systems. We prove that there is a superposition rule for solutions of such equations. This fact enables us to express the general solution of a dissipative Milne–Pinney equation in terms of particular solutions of a system of second-order linear differential equations and a set of constants.

scholarly journals On the boundary value problem with integral conditions for the systems of differential equations of second order

1967 ◽  
Vol 7 (1) ◽  
pp. 59-77
Author(s):  
B. Kvedaras
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Second Order ◽  
Integral Conditions ◽  
Systems Of Differential Equations

The abstracts (in two languages) can be found in the pdf file of the article. Original author name(s) and title in Russian and Lithuanian: Б. Кведарас. О краевой задаче с интегральными условиями обыкновенных дифференциальных уравнений B. Kvedaras. Apie kraštinį uždavinį su integralinėmis sąlygomis antros eilės diferencialinių lygčių sistemoms

MORE ON PARASUPERSYMMETRIES OF THE SCHRÖDINGER EQUATION

1993 ◽  
Vol 08 (05) ◽  
pp. 435-444 ◽  
Author(s):  
J. BECKERS ◽  
N. DEBERGH ◽  
A.G. NIKITIN
Keyword(s):  
Schrödinger Equation ◽  
Differential Equations ◽  
Schrodinger Equation ◽  
Interesting Case ◽  
Second Order ◽  
Schrödinger Equations ◽  
One Dimensional ◽  
Physical Systems ◽  
Systems Of Differential Equations ◽  
General Systems

One-dimensional spatial physical systems described by Schrödinger equations with time-independent interactions admit nth order parasupersymmetries. The general systems of differential equations for the parasupersymmetric operators are obtained and superposed with previous supersymmetric results. The interesting case of second order parasupersymmetries is completely solved.

scholarly journals Sturmian theorems for systems of differential equations

1980 ◽  
Vol 3 (1) ◽  
pp. 177-184
Author(s):  
C. Y. Chan
Keyword(s):  
Maximum Principle ◽  
Differential Equations ◽  
Second Order ◽  
Order Linear ◽  
Homogeneous Systems ◽  
Systems Of Differential Equations

Two Sturmian theorems are established for second order linear nonhomogeneous systems of two differential equations with the use of a maximum principle. The results also hold for homogeneous systems. For illustration, an example is given.

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