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 New Contractive Mappings and Their Fixed Points in Branciari Metric Spaces

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Hayel N. Saleh ◽  
Mohammad Imdad ◽  
Thabet Abdeljawad ◽  
Mohammad Arif
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fixed Points ◽  
Boundary Value Problems ◽  
Fourth Order ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Boundary Value ◽  
Contractive Mappings

In this paper, we introduce the notion of generalized L-contractions which enlarge the class of ℒ-contractions initiated by Cho in 2018. Thereafter, we also, define the notion of L∗-contractions. Utilizing our newly introduced notions, we establish some new fixed-point theorems in the setting of complete Branciari’s metric spaces, without using the Hausdorff assumption. Moreover, some examples and applications to boundary value problems of the fourth-order differential equations are given to exhibit the utility of the obtained results.

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