scholarly journals The Complementary q-Lidstone Interpolating Polynomials and Applications

2020 ◽  
Vol 25 (2) ◽  
pp. 34
Author(s):  
Zeinab Mansour ◽  
Maryam Al-Towailb
Keyword(s):  
Boundary Value Problems ◽  
Existence Of Solutions ◽  
Error Function ◽  
Boundary Value ◽  
Odd Order ◽  
Interpolating Polynomials

In this paper, we introduce the complementary q-Lidstone interpolating polynomial of degree 2 n , which involves interpolating data at the odd-order q-derivatives. For this polynomial, we will provide a q-Peano representation of the error function. Next, we use these results to prove the existence of solutions of the complementary q-Lidstone boundary value problems. Some examples are included.

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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