# Entire Solutions of Linear Systems of Moment Differential Equations and Related Asymptotic Growth at Infinity

@article{Lastra2022EntireSO, title={Entire Solutions of Linear Systems of Moment Differential Equations and Related Asymptotic Growth at Infinity}, author={Alberto Lastra}, journal={Differential Equations and Dynamical Systems}, year={2022} }

The general entire solution to a linear system of moment differential equations is obtained in terms of a moment kernel function for generalized summability, and the Jordan decomposition of the matrix defining the problem. The growth at infinity of any solution of the system is also determined, both globally and also following rays to infinity, determining the order and type of such solutions.

## References

SHOWING 1-10 OF 36 REFERENCES

Summability of Formal Solutions for Some Generalized Moment Partial Differential Equations

- Mathematics
- 2020

The concept of moment differentiation is extended to the class of moment summable functions, giving rise to moment differential properties. The main result leans on accurate upper estimates for the…

Analytic Solutions of Moment Partial Differential Equations with Constant Coefficients

- Mathematics
- 2013

We consider the Cauchy problem for linear moment partial differential equations with constant coefficients in two complex variables. We construct an integral representation of the solution of this…

Summability of Formal Solutions for a Family of Generalized Moment Integro-Differential Equations

- MathematicsFractional Calculus and Applied Analysis
- 2021

Generalized summability results are obtained regarding formal solutions of certain families of linear moment integro-differential equations with time variable coefficients. The main result leans on…

Multisummability of formal solutions of inhomogeneous linear partial differential equations with constant coefficients

- Mathematics
- 2012

We consider the Cauchy problem for a general inhomogeneous linear partial differential equation with constant coefficients in two complex variables. We obtain necessary and sufficient conditions for…

The Stokes Phenomenon for Some Moment Partial Differential Equations

- MathematicsJournal of Dynamical and Control Systems
- 2018

We study the Stokes phenomenon for the solutions of general homogeneous linear moment partial differential equations with constant coefficients in two complex variables under condition that the…

Strongly Regular Multi-level Solutions of Singularly Perturbed Linear Partial Differential Equations

- Mathematics
- 2015

We study the asymptotic behavior of the solutions related to a family of singularly perturbed partial differential equations in the complex domain. The analytic solutions are asymptotically…

Formal Power Series and Linear Systems of Meromorphic Ordinary Differential Equations

- Mathematics
- 1999

Basic Properties of Solutions.- Singularities of First Kind.- Highest-Level Formal Solutions.- Asymptotic Power Series.- Integral Operators.- Summable Power Series.- Cauchy-Heine Transform.-…

On stability analysis of semi‐linear fractional differential systems

- MathematicsMathematical Methods in the Applied Sciences
- 2019

In this article, new trends of analysis on existence, uniqueness, and stability of solution for semi‐linear fractional systems are considered. The results are based on a generalization of Bihari's…

Asymptotic Analysis and Summability of Formal Power Series

- Mathematics
- 2017

For many problems (ODEs, PDEs, difference equations, etc.) it makes sense to look for formal power series solutions which, if found, could well be divergent. However, these formal solutions will…

Gevrey Order of Formal Power Series Solutions of Inhomogeneous Partial Differential Equations with Constant Coefficients

- Mathematics
- 2010

In an earlier paper, the first author showed that certain normalized formal solutions of homogeneous linear partial differential equations with constant coefficients are multisummable, with a…