On a Class of Integro-Differential Equations in the Singular Case

2021 ◽  
Vol 57 (7) ◽  
pp. 857-867
Author(s):  
N. S. Gabbasov
Keyword(s):  
Differential Equations ◽  
Singular Case

scholarly journals Comparison theorems for ultrahyperbolic equations

1978 ◽  
Vol 1 (1) ◽  
pp. 31-40 ◽  
Author(s):  
C. C. Travis ◽  
E. C. Young
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Comparison Theorems ◽  
Singular Case ◽  
Partial Differential

Sturmian comparison theorems are obtained for solutions of a class of normal and singular ultrahyperbolic partial differential equations. In the singular case, solutions are considered which satisfy non-standard boundary conditions.

GEOMETRIC ASPECTS OF TIME-DEPENDENT SINGULAR DIFFERENTIAL EQUATIONS

2005 ◽  
Vol 02 (04) ◽  
pp. 597-618 ◽  
Author(s):  
XAVIER GRÀCIA ◽  
RUBÉN MARTÍN
Keyword(s):  
Differential Equations ◽  
Autonomous System ◽  
Time Dependent ◽  
Lagrangian Systems ◽  
Singular Matrix ◽  
Singular Case ◽  
Jet Bundle ◽  
Geometric Framework ◽  
Affine Spaces ◽  
Autonomous Case

A geometric framework for describing and solving time-dependent implicit differential equations F(t,x,x′) = 0 is studied, paying special attention to the linearly singular case, where F is affine in the velocities: A(t,x)x′ = b(t,x). This framework is based on the jet bundle of a time-dependent configuration space, and is an extension of the geometric framework of the autonomous case. When A is a singular matrix, the solutions can be obtained by means of constraint algorithms, either directly or through an equivalent autonomous system that can be constructed using the vector hull functor of affine spaces. As applications, we consider the jet bundle description of time-dependent lagrangian systems and the Skinner–Rusk formulation of time-dependent mechanics.

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