Three-point boundary value problems for nonlinear second-order impulsive q -difference equations
TL;DR: In this article, the authors prove existence and uniqueness results for nonlinear second-order impulsive qk-difference three-point boundary value problems, by using Banach's contraction mapping principle and Krasnoselskii's fixed-point theorem.
read more
Abstract: The quantum calculus on finite intervals was studied recently by the authors in Adv. Differ. Equ. 2013:282, 2013, where the concepts of qk-derivative and qk-integral of a function f : Jk := [tk, tk+1] → R have been introduced. In this paper, we prove existence and uniqueness results for nonlinear second-order impulsive qk-difference three-point boundary value problems, by using Banach’s contraction mapping principle and Krasnoselskii’s fixed-point theorem. MSC: 26A33; 39A13; 34A37
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Citations
Positive Solutions for a Three-Point Boundary Value Problem of Fractional Q-Difference Equations
TL;DR: By using fixed point theorems on mixed monotone operators, some sufficient conditions that guarantee the existence and uniqueness of positive solutions are given and an iterative scheme can be made to approximate the unique solution.
14
Impulsive quantum difference systems with boundary conditions
TL;DR: In this paper, the existence and uniqueness of solutions for coupled systems of nonlinear impulsive quantum difference equations with coupled and uncoupled boundary conditions were established by Banach's contraction principle and derived by using Leray-Schauder's alternative.
On a p ( x ) $p(x)$ -biharmonic problem with Navier boundary condition
TL;DR: In this paper, a bounded domain with Navier boundary condition was studied and the results of existence and non-existence of solutions were established by variational methods, and the authors established the results for existence and nonexistence of solutions.
References
Theory of Impulsive Differential Equations
V. Lakshmikantham,Д. Д. Байнов,P. S. Simeonov +2 more
- 01 May 1989
TL;DR: Theory of impulsive differential equations describes evolution processes with abrupt state changes due to short-term perturbations acting instantaneously.
4.4K
Impulsive differential equations
Anatolii M. Samoilenko,N A Perestyuk +1 more
- 01 Aug 1995
TL;DR: General description of impulsive differential systems linear systems stability of solutions periodic and almost periodic impulsive systems integral sets ofImpulsive systems optimal control in Impulsive systems asymptotic study of oscillations in impulsive system.
1.9K
Positive solutions for boundary value problem of nonlinear fractional differential equation
Zhanbing Bai,Haishen Lü +1 more
TL;DR: In this paper, the positive solution of nonlinear fractional difier- ential equation with semi-positive nonlinearity was investigated and the existence results of positive solution were obtained by using Krasnosel'skii flxed point theorem.
1.1K
Impulsive Differential Equations and Inclusions
Mouffak Benchohra,Johnny Henderson,Sotiris K. Ntouyas +2 more
- 01 Jan 2006
TL;DR: Ben-chohra as discussed by the authors dedicates this book to his family members who complete us, and his children, Mohamed, Maroua, and Abdelillah; J. Henderson dedicates to his wife, Darlene and his descendants, Kathy.
1K
Quantum calculus on finite intervals and applications to impulsive difference equations
TL;DR: In this paper, the authors define the qk-derivative and qkintegral of a function and prove their basic properties, and prove existence and uniqueness results for initial value problems for first and second-order impulsive qkdifference equations.