Impulsive Boundary Value Problems Research Articles

Study of three-point impulsive boundary value problems governed by $$\Psi $$-Caputo fractional derivative

Study of three-point impulsive boundary value problems governed by $$\Psi $$-Caputo fractional derivative

Correction to: Weakly Perturbed Impulsive Boundary-Value Problem for Integrodifferential Systems in the Resonance Case

Correction to: Weakly Perturbed Impulsive Boundary-Value Problem for Integrodifferential Systems in the Resonance Case

Quantum calculus with respect to another function

<abstract><p>In this paper, we studied the generalizations of quantum calculus on finite intervals. We presented the new definitions of the quantum derivative and quantum integral of a function with respect to another function and studied their basic properties. We gave an application of these newly defined quantum calculi by obtaining a new Hermite-Hadamard inequality for a convex function. Moreover, an impulsive boundary value problem involving quantum derivative, with respect to another function, was studied via the Banach contraction mapping principle.</p></abstract>

Impulsive Boundary-Value Problem for the Lyapunov Equation with Values in Hilbert Space

Impulsive Boundary-Value Problem for the Lyapunov Equation with Values in Hilbert Space

Correction to: Weakly Perturbed Impulsive Boundary-Value Problem for Integrodifferential Systems in the Resonance Case

Correction to: Weakly Perturbed Impulsive Boundary-Value Problem for Integrodifferential Systems in the Resonance Case

Existence of solutions for impulsive boundary value problems on infinite intervals

The paper deals with the existence of solutions for a general class of second-order nonlinear impulsive boundary value problems defined on an infinite interval. The main innovative aspects of the study are that the results are obtained under relatively mild conditions and the use of principal and nonprincipal solutions that were obtained in a very recent study. Additional results about the existence of bounded solutions are also provided, and theoretical results are supported by an illustrative example.

Instantaneous and Non-Instantaneous Impulsive Boundary Value Problem Involving the Generalized ψ-Caputo Fractional Derivative

This paper studies a new class of instantaneous and non-instantaneous impulsive boundary value problem involving the generalized ψ-Caputo fractional derivative with a weight. Depending on critical point theorems and some properties of ψ-Caputo-type fractional integration and differentiation, the variational construction and multiplicity result of solutions are established.

Multiterm Impulsive Caputo–Hadamard Type Differential Equations of Fractional Variable Order

In this study, we deal with an impulsive boundary value problem (BVP) for differential equations of variable fractional order involving the Caputo–Hadamard fractional derivative. The fundamental problems of existence and uniqueness of solutions are studied, and new existence and uniqueness results are established in the form of two fixed point theorems. In addition, Ulam–Hyers stability sufficient conditions are proved illustrating the suitability of the derived fundamental results. The obtained results are supported also by an example. Finally, the conclusion notes are highlighted.

A novel kernel functions algorithm for solving impulsive boundary value problems

In this letter, to fit the character of solutions to impulsive boundary value problems (IBVPs), we firstly construct a piecewise continuous space using the reproducing kernel function (RKF) of smooth reproducing kernel Hilbert space (RKHS) W3. Then we present a fourth order convergent collocation approach for IBVPs by using the piecewise continuous basis functions yielded by RKFs in W3. Also, the convergence order of our approach is proved. The accuracy and convergence order are shown numerically.

Existence of solutions for odd-order multi-point impulsive boundary value problems on time scales

Abstract Using a fixed point theorem due to Schaefer, the existence of solutions for an odd-order m-point impulsive boundary value problem on time scales is obtained. The problem considered is of general form, where both the differential equation and the impulse effects are nonlinear. Illustrative examples are provided.

Scattering analysis of a quantum impulsive boundary value problem with spectral parameter

We are interested in scattering and spectral analysis of an impulsive boundary value problem (IBVP) generated with a $q$-difference equation with eigenparameter in boundary condition in addition to impulsive conditions. We work on the Jost solution and scattering function of this problem, and by using the scattering solutions, we establish the resolvent operator, continuous spectrum and point spectrum of this problem. Furthermore, we discuss asymptotic behavior of the Jost solution and properties of eigenvalues.Also, we illustrate our results by a detailed example which is the special case of main problem.

Existence of solutions for third order multi point impulsive boundary value problems on time scales

In this paper, we obtain sufficient conditions for existence of solutions of a third order m-point impulsive boundary value problem on time scales. To the best of our knowledge, there is hardly any work dealing with third order multi point dynamic impulsive BVPs. The reason may be the complex arguments caused by both impulsive perturbations and calculations on time scales. As an application, we give an example demonstrating our results.

Infinitely Many Solutions to a Fourth-Order Impulsive Differential Equation with Two Control Parameters

In this article, we give some new criteria to guarantee the infinitely many solutions for a fourth-order impulsive boundary value problem. Our main tool to ensure the existence of infinitely many solutions is the classical Ricceri’s Variational Principle.

Existence and nonexistence of positive solutions for the second-order m-point eigenvalue impulsive boundary value problem

This paper is devoted to the study of the existence and nonexistence of positive solutions for a second-order m-point eigenvalue impulsive boundary value problem. We use the fixed point theorems on the cones in order to achieve our results.

"Existence of solutions for an impulsive boundary value problem with nonlinear derivative dependence on unbounded intervals via variational methods"

"In this paper, we employ the critical point theory and iterative methods to establish the existence of solutions for an impulsive boundary value problem with nonlinear derivative dependence on the half-line."

On the mixed fractional quantum and Hadamard derivatives for impulsive boundary value problems

AbstractIn this work, we initiate the study of a new class of impulsive boundary value problems consisting of mixed type fractional quantum and Hadamard derivatives. We will establish existence and uniqueness results by using tools from the functional analysis. We prove the uniqueness result via Banach’s contraction mapping principle, while we will use the Leray-Schauder nonlinear alternative to establish an existence result. We also present examples to illustrate the obtained results.

Scattering Function and The Resolvent of The Impulsive Boundary Value Problem

The purpose of this study is to examine the properties of scattering solutions and the scattering function of an impulsive Sturm-Liouville boundary value problem on the semi axis. By using Jost solutions, we obtain the scattering function, asymptotic representation of Jost function and resolvent operator. Finally, we study scattering solutions and scattering function of an unperturbated impulsive equation.

Seminonoscillation Intervals and Sign-Constancy of Green’s Functions of Two-Point Impulsive Boundary-Value Problems

Seminonoscillation Intervals and Sign-Constancy of Green’s Functions of Two-Point Impulsive Boundary-Value Problems

On Impulsive Boundary Value Problem with Riemann-Liouville Fractional Order Derivative

Our manuscript is devoted to investigating a class of impulsive boundary value problems under the concept of the Riemann-Liouville fractional order derivative. The subject problem is of implicit type. We develop some adequate conditions for the existence and puniness of a solution to the proposed problem. For our required results, we utilize the classical fixed point theorems from Banach and Scheafer. It is to be noted that the impulsive boundary value problem under the fractional order derivative of the Riemann-Liouville type has been very rarely considered in literature. Finally, to demonstrate the obtained results, we provide some pertinent examples.

Semi-nonoscillation intervals and sign-constancy of Green’s functions of two-point impulsive boundary-value problems

UDC 517.9 We consider the second order impulsive differential equation with delays where for In this paper, we obtain the conditions of semi-nonoscillation for the corresponding homogeneous equation on the interval Using these results, we formulate theorems on sign-constancy of Green's functions for two-point impulsive boundary-value problems in terms of differential inequalities.