scholarly journals Impulsive Boundary Value Problems for Planar Hamiltonian Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Zeynep Kayar ◽  
Ağacık Zafer
Keyword(s):  
Boundary Value Problem ◽  
Hamiltonian Systems ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Type Inequality ◽  
Existence And Uniqueness Theorem ◽  
Uniqueness Of Solutions ◽  
Impulsive Boundary Value Problems ◽  
Impulsive Boundary Value Problem ◽  
Lyapunov Type Inequality

We give an existence and uniqueness theorem for solutions of inhomogeneous impulsive boundary value problem (BVP) for planar Hamiltonian systems. Green's function that is needed for representing the solutions is obtained and its properties are listed. The uniqueness of solutions is connected to a Lyapunov type inequality for the corresponding homogeneous BVP.

scholarly journals Existence and uniqueness of solutions for a mixed p-Laplace boundary value problem involving fractional derivatives

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Shuqi Wang ◽  
Zhanbing Bai
Keyword(s):  
Boundary Value Problem ◽  
Existence And Uniqueness ◽  
Fractional Derivatives ◽  
Boundary Value ◽  
Contraction Mapping Principle ◽  
Uniqueness Of Solutions ◽  
Novel Approach ◽  
Banach Contraction ◽  
Left And Right ◽  
Banach Contraction Mapping Principle

AbstractIn this article, the existence and uniqueness of solutions for a multi-point fractional boundary value problem involving two different left and right fractional derivatives with p-Laplace operator is studied. A novel approach is used to acquire the desired results, and the core of the method is Banach contraction mapping principle. Finally, an example is given to verify the results.

scholarly journals POSITIVE SOLUTIONS OF A SECOND-ORDER NEUMANN BOUNDARY VALUE PROBLEM WITH A PARAMETER

2012 ◽  
Vol 86 (2) ◽  
pp. 244-253 ◽  
Author(s):  
YANG-WEN ZHANG ◽  
HONG-XU LI
Keyword(s):  
Boundary Value Problem ◽  
Positive Solutions ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Neumann Boundary ◽  
Existence And Uniqueness Theorem ◽  
Neumann Boundary Value Problem ◽  
Image Position ◽  
Continuous Dependence Of Solutions

AbstractIn this paper, we consider the Neumann boundary value problem with a parameter λ∈(0,∞): By using fixed point theorems in a cone, we obtain some existence, multiplicity and nonexistence results for positive solutions in terms of different values of λ. We also prove an existence and uniqueness theorem and show the continuous dependence of solutions on the parameter λ.

scholarly journals RETRACTED ARTICLE: Existence and uniqueness of solutions for the Schrödinger integrable boundary value problem

2018 ◽  
Vol 2018 (1) ◽  
Author(s):  
Jianjie Wang ◽  
Ali Mai ◽  
Hong Wang
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Point Theorem ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Uniqueness Of Solutions ◽  
Linear Maps ◽  
Retracted Article

Abstract This paper is mainly devoted to the study of one kind of nonlinear Schrödinger differential equations. Under the integrable boundary value condition, the existence and uniqueness of the solutions of this equation are discussed by using new Riesz representations of linear maps and the Schrödinger fixed point theorem.

scholarly journals The Existence and Uniqueness of Solutions and Lyapunov-Type Inequality for CFR Fractional Differential Equations

2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
Xia Wang ◽  
Run Xu
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Type Inequality ◽  
Uniqueness Theorems ◽  
Initial Value ◽  
Uniqueness Of Solutions ◽  
Maximum Value ◽  
Fractional Differential ◽  
Lyapunov Type Inequality

In this paper, we research CFR fractional differential equations with the derivative of order 3<α<4. We prove existence and uniqueness theorems for CFR-type initial value problem. By Green’s function and its corresponding maximum value, we obtain the Lyapunov-type inequality of corresponding equations. As for application, we study the eigenvalue problem in the sense of CFR.

scholarly journals Solvability of a fourth order boundary value problem with periodic boundary conditions

1988 ◽  
Vol 11 (2) ◽  
pp. 275-284
Author(s):  
Chaitan P. Gupta
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Fourth Order ◽  
Existence And Uniqueness ◽  
Periodic Boundary ◽  
Boundary Value ◽  
Elastic Beam ◽  
Periodic Boundary Conditions ◽  
Uniqueness Of Solutions

Fourth order boundary value problems arise in the study of the equilibrium of an elastaic beam under an external load. The author earlier investigated the existence and uniqueness of the solutions of the nonlinear analogues of fourth order boundary value problems that arise in the equilibrium of an elastic beam depending on how the ends of the beam are supported. This paper concerns the existence and uniqueness of solutions of the fourth order boundary value problems with periodic boundary conditions.

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