scholarly journals Lyapunov-type inequality for a class of odd-order differential equations

2010 ◽  
Vol 234 (10) ◽  
pp. 2962-2968 ◽  
Author(s):  
Xiaojing Yang ◽  
Yong-In Kim ◽  
Kueiming Lo
Keyword(s):  
Differential Equations ◽  
Type Inequality ◽  
Odd Order ◽  
Lyapunov Type Inequality

scholarly journals The Existence and Uniqueness of Solutions and Lyapunov-Type Inequality for CFR Fractional Differential Equations

2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
Xia Wang ◽  
Run Xu
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Type Inequality ◽  
Uniqueness Theorems ◽  
Initial Value ◽  
Uniqueness Of Solutions ◽  
Maximum Value ◽  
Fractional Differential ◽  
Lyapunov Type Inequality

In this paper, we research CFR fractional differential equations with the derivative of order 3<α<4. We prove existence and uniqueness theorems for CFR-type initial value problem. By Green’s function and its corresponding maximum value, we obtain the Lyapunov-type inequality of corresponding equations. As for application, we study the eigenvalue problem in the sense of CFR.

scholarly journals Lyapunov-type inequality for third-order half-linear differential equations

2013 ◽  
Vol 44 (4) ◽  
pp. 351-357 ◽  
Author(s):  
Jozef Kiselak
Keyword(s):  
Differential Equations ◽  
Type Inequality ◽  
Linear Differential Equations ◽  
Third Order ◽  
Linear Differential ◽  
Lyapunov Type Inequality

In this paper, we give a proof of a Lyapunov-type inequality for third-order half-linear differential equations. Then some applications, e.g.~the distance between consecutive zeros of a solution, are studied with the help of the inequality.

scholarly journals Nonzero Solutions for Nonlinear Systems of Fourth-Order Boundary Value Problems

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Ravi P. Agarwal ◽  
Mohamed Jleli ◽  
Bessem Samet
Keyword(s):  
Nonlinear Systems ◽  
Differential Equations ◽  
Boundary Value Problems ◽  
Fourth Order ◽  
Boundary Value ◽  
Type Inequality ◽  
Matrix Analysis ◽  
Necessary Condition ◽  
Generalized Eigenvalues ◽  
Lyapunov Type Inequality

This study is devoted to the investigation of nonlinear systems of fourth-order boundary value problems. Namely, using some techniques from matrix analysis and ordinary differential equations, a Lyapunov-type inequality providing a necessary condition for the existence of nonzero solutions is obtained. Next, an estimate involving generalized eigenvalues is derived as an application of our main result.

scholarly journals Analysis of some Katugampola fractional differential equations with fractional boundary conditions

2021 ◽  
Vol 18 (6) ◽  
pp. 7269-7279
Author(s):  
Barbara Łupińska ◽  
◽  
Ewa Schmeidel
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Boundary Problem ◽  
Fractional Differential Equations ◽  
Type Inequality ◽  
Fractional Differential ◽  
Fractional Boundary Conditions ◽  
Lyapunov Type Inequality

<abstract><p>In this work, some class of the fractional differential equations under fractional boundary conditions with the Katugampola derivative is considered. By proving the Lyapunov-type inequality, there are deduced the conditions for existence, and non-existence of the solutions to the considered boundary problem. Moreover, we present some examples to demonstrate the effectiveness and applications of the new results.</p></abstract>

scholarly journals New Results for Oscillation of Solutions of Odd-Order Neutral Differential Equations

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1095
Author(s):  
Clemente Cesarano ◽  
Osama Moaaz ◽  
Belgees Qaraad ◽  
Nawal A. Alshehri ◽  
Sayed K. Elagan ◽  
...  
Keyword(s):  
Differential Equations ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Oscillatory Behavior ◽  
Neutral Delay ◽  
Neutral Differential Equations ◽  
Odd Order ◽  
Future Prediction ◽  
Functional Differential ◽  
Delay Differential

Differential equations with delay arguments are one of the branches of functional differential equations which take into account the system’s past, allowing for more accurate and efficient future prediction. The symmetry of the equations in terms of positive and negative solutions plays a fundamental and important role in the study of oscillation. In this paper, we study the oscillatory behavior of a class of odd-order neutral delay differential equations. We establish new sufficient conditions for all solutions of such equations to be oscillatory. The obtained results improve, simplify and complement many existing results.

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