A result on a singular Cauchy problem with a radial point revisited using microdifferential calculus

2018 ◽  
Vol 140 ◽  
pp. 45-68
Author(s):  
Alexander Getmanenko
Keyword(s):  
Cauchy Problem ◽  
Singular Cauchy Problem

Nonuniqueness Theorem for a Singular Cauchy Problem

2000 ◽  
Vol 7 (2) ◽  
pp. 317-327 ◽  
Author(s):  
Josef Kalas
Keyword(s):  
Cauchy Problem ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Lyapunov Functions ◽  
Singular Cauchy Problem ◽  
Vector Lyapunov Functions

Abstract A general nonuniqueness theorem is given for ordinary differential equations with singularities. The criterion uses vector Lyapunov functions and extends the previously known criteria ones. The applicability is illustrated by several examples.

scholarly journals Singular Cauchy problem for the general Euler-Poisson-Darboux equation

2018 ◽  
Vol 16 (1) ◽  
pp. 23-31 ◽  
Author(s):  
E.L. Shishkina
Keyword(s):  
Cauchy Problem ◽  
Bessel Operator ◽  
Singular Cauchy Problem ◽  
Darboux Equation

AbstractIn this paper we obtain the solution of the singular Cauchy problem for the Euler-Poisson-Darboux equation when differential Bessel operator acts by each variable.

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