scholarly journals An existence and uniqueness result for linear fractional impulsive boundary value problems as an application of Lyapunov type inequality

2017 ◽  
Vol 4 (46) ◽  
Author(s):  
Zeynep Kayar
Keyword(s):  
Boundary Value Problems ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Type Inequality ◽  
Uniqueness Result ◽  
Impulsive Boundary Value Problems ◽  
Lyapunov Type Inequality

scholarly journals Impulsive Boundary Value Problems for Planar Hamiltonian Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Zeynep Kayar ◽  
Ağacık Zafer
Keyword(s):  
Boundary Value Problem ◽  
Hamiltonian Systems ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Type Inequality ◽  
Existence And Uniqueness Theorem ◽  
Uniqueness Of Solutions ◽  
Impulsive Boundary Value Problems ◽  
Impulsive Boundary Value Problem ◽  
Lyapunov Type Inequality

We give an existence and uniqueness theorem for solutions of inhomogeneous impulsive boundary value problem (BVP) for planar Hamiltonian systems. Green's function that is needed for representing the solutions is obtained and its properties are listed. The uniqueness of solutions is connected to a Lyapunov type inequality for the corresponding homogeneous BVP.

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 A New Proof for Lyapunov-Type Inequality on the Fractional Boundary Value Problem

Symmetry ◽  
2020 ◽  
Vol 13 (1) ◽  
pp. 29
Author(s):  
Yumei Zou ◽  
Xin Zhang ◽  
Hongyu Li
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Green’S Function ◽  
Boundary Value Problems ◽  
Green's Function ◽  
Boundary Value ◽  
Type Inequality ◽  
Fractional Boundary Value Problem ◽  
Lyapunov Type Inequality ◽  
Fractional Boundary Value Problems

In this article, some new Lyapunov-type inequalities for a class of fractional boundary value problems are established by use of the nonsymmetry property of Green’s function corresponding to appropriate boundary conditions.

scholarly journals Best proximity point theorems for cyclic p-contractions with some consequences and applications

2021 ◽  
Vol 26 (1) ◽  
pp. 113-129
Author(s):  
Mustafa Aslantas ◽  
Hakan Sahin ◽  
Ishak Altun
Keyword(s):  
Fixed Point ◽  
Boundary Value Problems ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Best Proximity Point ◽  
Boundary Value ◽  
Uniqueness Result ◽  
Second Order ◽  
Common Solution

In this paper, we introduce the concept of cyclic p-contraction pair for single-valued mappings. Then we present some best proximity point results for such mappings defined on proximally complete pair of subsets of a metric space. Also, we provide some illustrative examples that compared our results with some earliest. Finally, by taking into account a fixed point consequence of our main result we give an existence and uniqueness result for a common solution of a system of second order boundary value problems.

scholarly journals Existence and uniqueness criteria for the higher-order Hilfer fractional boundary value problems at resonance

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Yousef Gholami
Keyword(s):  
Boundary Value Problems ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Higher Order ◽  
Coupled Systems ◽  
At Resonance ◽  
Uniqueness Criteria ◽  
Fractional Boundary Value Problems

Abstract This investigation is devoted to the study of a certain class of coupled systems of higher-order Hilfer fractional boundary value problems at resonance. Combining the coincidence degree theory with the Lipschitz-type continuity conditions on nonlinearities, we present some existence and uniqueness criteria. Finally, to practically implement the obtained theoretical criteria, we give an illustrative application.

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