scholarly journals A Unified Integral Equation Scheme for Doubly Periodic Laplace and Stokes Boundary Value Problems in Two Dimensions

2018 ◽  
Vol 71 (11) ◽  
pp. 2334-2380 ◽  
Author(s):  
Alex H. Barnett ◽  
Gary R. Marple ◽  
Shravan Veerapaneni ◽  
Lin Zhao
Keyword(s):  
Integral Equation ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Two Dimensions

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.

Sign in / Sign up

Export Citation Format

Share Document