Lyapunov-type inequality for a class of even-order differential equations

2010 ◽  
Vol 215 (11) ◽  
pp. 3884-3890 ◽  
Author(s):  
Xiaojing Yang ◽  
Kueiming Lo
Keyword(s):  
Differential Equations ◽  
Type Inequality ◽  
Even 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>

A nonlocal problem for a differential operator of even order with involution

2020 ◽  
Vol 26 (2) ◽  
pp. 297-307
Author(s):  
Petro I. Kalenyuk ◽  
Yaroslav O. Baranetskij ◽  
Lubov I. Kolyasa
Keyword(s):  
Differential Operator ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Riesz Basis ◽  
Existence And Uniqueness ◽  
Spectral Properties ◽  
Nonlocal Problem ◽  
Even Order

AbstractWe study a nonlocal problem for ordinary differential equations of {2n}-order with involution. Spectral properties of the operator of this problem are analyzed and conditions for the existence and uniqueness of its solution are established. It is also proved that the system of eigenfunctions of the analyzed problem forms a Riesz basis.

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