scholarly journals On the well-posedness of the Cauchy problem for differential equations with distributed prehistory considering delay function perturbations

2016 ◽  
Vol 170 (1) ◽  
pp. 7-18 ◽  
Author(s):  
Phridon Dvalishvili ◽  
Tamaz Tadumadze
Keyword(s):  
Cauchy Problem ◽  
Differential Equations ◽  
Well Posedness ◽  
Delay Function ◽  
The Cauchy Problem

ON THE CAUCHY PROBLEM FOR SOME PSEUDO-DIFFERENTIAL EQUATIONS OF SCHRÖDINGER TYPE

1996 ◽  
Vol 06 (03) ◽  
pp. 295-314 ◽  
Author(s):  
R. AGLIARDI ◽  
D. MARI
Keyword(s):  
Differential Equation ◽  
Cauchy Problem ◽  
Fundamental Solution ◽  
Differential Equations ◽  
Lower Order ◽  
Order Term ◽  
Well Posedness ◽  
Gevrey Spaces ◽  
The Cauchy Problem ◽  
Pseudo Differential Equation

A fundamental solution of the Cauchy problem is constructed for a pseudo-differential equation generalizing some Schrödinger equations. Then well-posedness of the Cauchy problem is proved in some Gevrey spaces whose indices depend on the lower order term of the operator.

Global well-posedness of the Cauchy problem for system of oscillators on 2D-lattice with power potentials

2019 ◽  
Vol 16 (4) ◽  
pp. 465-476 ◽  
Author(s):  
Sergiy Bak
Keyword(s):  
Cauchy Problem ◽  
Differential Equations ◽  
Existence And Uniqueness ◽  
Infinite System ◽  
Global Solutions ◽  
Nonlinear Oscillators ◽  
Well Posedness ◽  
Two Dimensional ◽  
Coupled Nonlinear Oscillators ◽  
The Cauchy Problem

We consider an infinite system of ordinary differential equations that describes the dynamics of an infinite system of linearly coupled nonlinear oscillators on a two-dimensional integer-valued lattice. We prove a result on the existence and uniqueness of global solutions of the Cauchy problem for such systems with power potentials. Moreover, a result on the nonexistence of global solutions is obtained.

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