First integrals and Darboux polynomials of homogeneous linear differential systems

1995 ◽  
pp. 469-484 ◽  
Author(s):  
Jacques-Arthur Weil
Keyword(s):  
First Integrals ◽  
Differential Systems ◽  
Darboux Polynomials ◽  
Linear Differential Systems ◽  
Linear Differential ◽  
Homogeneous Linear

scholarly journals General iterative methods for nonlinear boundary value problems

1995 ◽  
Vol 37 (1) ◽  
pp. 58-85 ◽  
Author(s):  
Radha Shridharan ◽  
Ravi P. Agarwal
Keyword(s):  
Boundary Value Problems ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Nonlinear Boundary Value Problems ◽  
Constructive Theory ◽  
Differential Systems ◽  
Linear Differential Systems ◽  
Nonlinear Boundary Value ◽  
Linear Differential ◽  
Homogeneous Linear

AbstractIn this paper we shall develop existence-uniqueness as well as constructive theory for the solutions of systems of nonlinear boundary value problems when only approximations of the fundamental matrix of the associated homogeneous linear differential systems are known. To make the analysis widely applicable, all the results are proved component-wise. An illustration which dwells upon the sharpness as well as the importance of the obtained results is also presented.

scholarly journals Crossing Periodic Orbits via First Integrals

2020 ◽  
Vol 30 (11) ◽  
pp. 2050163
Author(s):  
Jaume Llibre ◽  
Durval José Tonon ◽  
Mariana Queiroz Velter
Keyword(s):  
Periodic Orbits ◽  
First Integrals ◽  
The Other ◽  
Differential Systems ◽  
Linear Differential Systems ◽  
Families Of Periodic Orbits ◽  
Linear Differential ◽  
Nonlinear Differential Systems

We characterize the families of periodic orbits of two discontinuous piecewise differential systems in [Formula: see text] separated by a plane using their first integrals. One of these discontinuous piecewise differential systems is formed by linear differential systems, and the other by nonlinear differential systems.

M(λ)-computation for singular differential systems

1989 ◽  
Vol 112 (3-4) ◽  
pp. 327-330
Author(s):  
Hans G. Kaper ◽  
Allan M. Krall
Keyword(s):  
Initial Data ◽  
Fundamental Matrix ◽  
Second Order ◽  
Bilinear Transformation ◽  
Order Problem ◽  
Differential Systems ◽  
Linear Differential Systems ◽  
Linear Differential ◽  
Homogeneous Linear

SynopsisDepending upon the initial data associated with the fundamental matrix, the function M(λ), used to generate L2-solutions of homogeneous linear differential systems, may vary. We show that there is a matrix bilinear transformation between such functions M(λ) with different initial data and illustrate how the result can be used to simplify the calculation of a specific M(λ)-function for a scalar second-order problem.

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