scholarly journals "A spectral criterion for the existence of the stabilizing solution of a class of Riccati type differential equations with periodic coefficients"

2021 ◽  
Vol 66 (1) ◽  
pp. 159-177
Author(s):  
Vasile Dragan ◽  
Ioan-Lucian Popa
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Nonlinear Differential Equation ◽  
Continuous Time ◽  
Existence And Uniqueness ◽  
Control Problems ◽  
Linear Quadratic ◽  
Stabilizing Solution ◽  
Spectral Criterion ◽  
Special Cases

"In this paper, we investigate the existence and uniqueness of a stabilizing solution to a periodic backward nonlinear differential equation. This class of nonlinear equations includes as special cases many of the continuous-time Riccati equations arising both in deterministic and stochastic linear quadratic (LQ) type control problems."

scholarly journals On the correct formulation of a nonlinear differential equations in Banach space

2001 ◽  
Vol 26 (7) ◽  
pp. 437-444
Author(s):  
Mahmoud M. El-Borai ◽  
Osama L. Moustafa ◽  
Fayez H. Michael
Keyword(s):  
Differential Equation ◽  
Banach Space ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Nonlinear Differential Equation ◽  
Existence And Uniqueness ◽  
Initial Value Problems ◽  
Nonlinear Differential Equations ◽  
Initial Value ◽  
Correct Formulation

We study, the existence and uniqueness of the initial value problems in a Banach spaceEfor the abstract nonlinear differential equation(dn−1/dtn−1)(du/dt+Au)=B(t)u+f(t,W(t)), and consider the correct solution of this problem. We also give an application of the theory of partial differential equations.

Uniqueness Implies Existence and Uniqueness Conditions for a Class of (k + j)-Point Boundary Value Problems for n-th Order Differential Equations

2012 ◽  
Vol 55 (2) ◽  
pp. 285-296 ◽  
Author(s):  
Paul W. Eloe ◽  
Johnny Henderson ◽  
Rahmat Ali Khan
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Nonlinear Differential Equation ◽  
Unique Solvability ◽  
Existence And Uniqueness ◽  
Existence Results ◽  
Point Boundary ◽  
Uniqueness And Existence ◽  
Uniqueness And Existence Results

AbstractFor the n-th order nonlinear differential equation, y(n) = f (x, y, y′, … , y(n–1)), we consider uniqueness implies uniqueness and existence results for solutions satisfying certain (k + j)-point boundary conditions for 1 ≤ j ≤ n – 1 and 1 ≤ k ≤ n – j. We define (k; j)-point unique solvability in analogy to k-point disconjugacy and we show that (n – j0; j0)-point unique solvability implies (k; j)-point unique solvability for 1 ≤ j ≤ j0, and 1 ≤ k ≤ n – j. This result is analogous to n-point disconjugacy implies k-point disconjugacy for 2 ≤ k ≤ n – 1.

scholarly journals Some Study Methods for Ordinary Differential Equation Integrability of the Second Order of a Certain Type

2019 ◽  
pp. 48-62
Author(s):  
O. V. Zadorozhnaya ◽  
V. K. Kochetkov
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Nonlinear Differential Equation ◽  
Nonlinear Differential Equations ◽  
Practical Interest ◽  
Second Order ◽  
Parameter Method ◽  
Study Methods ◽  
Special Cases ◽  
General Conditions

The paper deals with treating some study methods of the equation integrability of a certain type that are little studied in the theory of differential equations. It is known that a significant part of the differential equations cannot be integrated. Then, to develop methods for their study is, certainly, of scientific interest. The obtained results, formulated as theorems and statements, are of scientific and practical interest because of their importance for applications in modern science.In the paper we present an alternative method for studying the integrability of both linear and nonlinear differential equations of the second order. An introduction of parameters allowed us to develop a study method for the integrability of ordinary differential equations of the second order. We also formulate the theorems describing some General conditions for the integrability of the second-order linear equation and consider special cases of integrability, which arise out of the above facts.Based on the obtained parameter method, some General conditions for the integrability of the nonlinear differential equation of the second order are given, and the consequences of these General conditions are indicated.We have obtained new results related to the construction and development of methods for studying the differential equation to which some types of differential equations are reduced and laid the foundations for a rigorous and systematic study of the introduced special nonlinear differential equation of the second order.

scholarly journals Boundedness of Solutions to Differential Equations of Fourth Order with Oscillatory Restoring and Forcing Terms

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Cemil Tunç ◽  
Muzaffer Ateş
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Nonlinear Differential Equation ◽  
Fourth Order ◽  
Cauchy Formula ◽  
Boundedness Of Solutions ◽  
Constant Coefficients ◽  
Particular Solution

This paper deals with the boundedness of solutions to a nonlinear differential equation of fourth order. Using the Cauchy formula for the particular solution of nonhomogeneous differential equations with constant coefficients, we prove that the solution and its derivatives up to order three are bounded.

scholarly journals Asymptotic Dichotomy in a Class of Third-Order Nonlinear Differential Equations with Impulses

2010 ◽  
Vol 2010 ◽  
pp. 1-20 ◽  
Author(s):  
Kun-Wen Wen ◽  
Gen-Qiang Wang ◽  
Sui Sun Cheng
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Nonlinear Differential Equation ◽  
Nonlinear Differential Equations ◽  
Functional Differential Equations ◽  
Higher Order ◽  
Third Order ◽  
Order Nonlinear Differential Equation ◽  
Functional Differential

Solutions of quite a few higher-order delay functional differential equations oscillate or converge to zero. In this paper, we obtain several such dichotomous criteria for a class of third-order nonlinear differential equation with impulses.

scholarly journals Kestabilan Model Epidemi SEIR Dengan Laju Insidensi

2015 ◽  
Vol 10 (2) ◽  
pp. 74
Author(s):  
Roni Tri Putra ◽  
Sukatik - ◽  
Sri Nita
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Incidence Rate ◽  
Epidemic Model ◽  
Existence And Uniqueness ◽  
Equation System ◽  
Differential Equation System ◽  
Equilibrium Existence

In this paper, it will be studied stability for a SEIR epidemic model with infectious force in latent, infected and immune period with incidence rate. From the model it will be found investigated the existence and uniqueness solution  of points its equilibrium. Existence solution of points equilibrium proved by show its differential equations system of equilibrium continue, and uniqueness solution of points equilibrium proved by show its differential equation system of equilibrium differentiable continue. 

scholarly journals Fuzzy Conformable Fractional Differential Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Atimad Harir ◽  
Said Melliani ◽  
Lalla Saadia Chadli
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Uniqueness Theorem ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Existence And Uniqueness Theorem ◽  
Fractional Differential ◽  
Fractional Differentiability ◽  
Derivatives Of ◽  
Fuzzy Fractional Differential Equation

In this study, fuzzy conformable fractional differential equations are investigated. We study conformable fractional differentiability, and we define fractional integrability properties of such functions and give an existence and uniqueness theorem for a solution to a fuzzy fractional differential equation by using the concept of conformable differentiability. This concept is based on the enlargement of the class of differentiable fuzzy mappings; for this, we consider the lateral Hukuhara derivatives of order q ∈ 0,1 .

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