scholarly journals Existence of Solutions for Weighted p(r)-Laplacian Impulsive Integro-Differential System Periodic-Like Boundary Value Problems

2010 ◽  
Vol 2010 ◽  
pp. 1-24
Author(s):  
Guizhen Zhi ◽  
Liang Zhao ◽  
Guangxia Chen ◽  
Shujuan Wang ◽  
Qihu Zhang
Keyword(s):  
Boundary Value Problems ◽  
Differential System ◽  
Existence Of Solutions ◽  
Boundary Value

scholarly journals Existence of solutions for functional boundary value problems at resonance on the half-line

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Bingzhi Sun ◽  
Weihua Jiang
Keyword(s):  
Boundary Value Problems ◽  
Banach Spaces ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Half Line ◽  
Projection Scheme ◽  
At Resonance ◽  
Functional Boundary

Abstract By defining the Banach spaces endowed with the appropriate norm, constructing a suitable projection scheme, and using the coincidence degree theory due to Mawhin, we study the existence of solutions for functional boundary value problems at resonance on the half-line with $\operatorname{dim}\operatorname{Ker}L = 1$ dim Ker L = 1 . And an example is given to show that our result here is valid.

scholarly journals The existence of solutions for Sturm–Liouville differential equation with random impulses and boundary value problems

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Zihan Li ◽  
Xiao-Bao Shu ◽  
Tengyuan Miao
Keyword(s):  
Differential Equation ◽  
Integral Equation ◽  
Differential Equations ◽  
Boundary Value Problems ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Lower Solution ◽  
Iterative Sequence ◽  
Random Impulses ◽  
Sturm Liouville

AbstractIn this article, we consider the existence of solutions to the Sturm–Liouville differential equation with random impulses and boundary value problems. We first study the Green function of the Sturm–Liouville differential equation with random impulses. Then, we get the equivalent integral equation of the random impulsive differential equation. Based on this integral equation, we use Dhage’s fixed point theorem to prove the existence of solutions to the equation, and the theorem is extended to the general second order nonlinear random impulsive differential equations. Then we use the upper and lower solution method to give a monotonic iterative sequence of the generalized random impulsive Sturm–Liouville differential equations and prove that it is convergent. Finally, we give two concrete examples to verify the correctness of the results.

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