scholarly journals First-Order Three-Point Boundary Value Problems at Resonance Part III

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Mesliza Mohamed ◽  
Bevan Thompson ◽  
Muhammad Sufian Jusoh
Keyword(s):  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Implicit Function Theorem ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Implicit Function ◽  
Point Boundary ◽  
First Order ◽  
At Resonance

The main purpose of this paper is to investigate the existence of solutions of BVPs for a very general case in which both the system of ordinary differential equations and the boundary conditions are nonlinear. By employing the implicit function theorem, sufficient conditions for the existence of three-point boundary value problems are established.

scholarly journals Solvability of Three-Point Boundary Value Problems at Resonance with ap-Laplacian on Finite and Infinite Intervals

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Hairong Lian ◽  
Patricia J. Y. Wong ◽  
Shu Yang
Keyword(s):  
Boundary Value Problems ◽  
Nonlinear Term ◽  
Order Differential Equation ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Point Boundary ◽  
First Order ◽  
At Resonance ◽  
Infinite Intervals

Three-point boundary value problems of second-order differential equation with ap-Laplacian on finite and infinite intervals are investigated in this paper. By using a new continuation theorem, sufficient conditions are given, under the resonance conditions, to guarantee the existence of solutions to such boundary value problems with the nonlinear term involving in the first-order derivative explicitly.

scholarly journals Boundary-Value Problems for Weakly Nonlinear Delay Differential Systems

2011 ◽  
Vol 2011 ◽  
pp. 1-19 ◽  
Author(s):  
A. Boichuk ◽  
J. Diblík ◽  
D. Khusainov ◽  
M. Růžičková
Keyword(s):  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Linear Part ◽  
Sufficient Conditions ◽  
Nonlinear Boundary Value Problems ◽  
Weakly Nonlinear ◽  
Delay Differential Systems ◽  
Delay Differential

Conditions are derived of the existence of solutions of nonlinear boundary-value problems for systems ofnordinary differential equations with constant coefficients and single delay (in the linear part) and with a finite number of measurable delays of argument in nonlinearity:ż(t)=Az(t-τ)+g(t)+εZ(z(hi(t),t,ε),  t∈[a,b], assuming that these solutions satisfy the initial and boundary conditionsz(s):=ψ(s) if s∉[a,b],  lz(⋅)=α∈Rm. The use of a delayed matrix exponential and a method of pseudoinverse by Moore-Penrose matrices led to anexplicitandanalyticalform of sufficient conditions for the existence of solutions in a given space and, moreover, to the construction of an iterative process for finding the solutions of such problems in a general case when the number of boundary conditions (defined by a linear vector functionall) does not coincide with the number of unknowns in the differential system with a single delay.

scholarly journals Kronecker Product of matrices and their applications to self-adjoint two-point boundary value problems associated with first order matrix differential systems

2021 ◽  
Vol 10 (10) ◽  
pp. 25399-25407
Author(s):  
Sriram Bhagavatula ◽  
Dileep Durani Musa ◽  
Murty Kanuri
Keyword(s):  
Boundary Value Problems ◽  
Kronecker Product ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Least Square ◽  
Point Boundary ◽  
Uniqueness Of Solutions ◽  
Differential Systems ◽  
First Order ◽  
Product Of Matrices

In this paper, we shall be concerned with Kronecker product or Tensor product of matrices and develop their properties in a systematic way. The properties of the Kronecker product of matrices is used as a tool to establish existence and uniqueness of solutions to two-point boundary value problems associated with system of first order differential systems. A new approach is described to solve the Kronecker product linear systems and establish best least square solutions to the problem. Several interesting examples are given to highlight the importance of Kronecker product of matrices. We present adjoint boundary value problems and deduce a set of necessary and sufficient conditions for the Kronecker product boundary value problem to be self-adjoint.

scholarly journals Existence of Solutions for Fractional Multi-Point Boundary Value Problems on an Infinite Interval at Resonance

Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 126
Author(s):  
Wei Zhang ◽  
Wenbin Liu
Keyword(s):  
Boundary Value Problems ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Existence Results ◽  
Infinite Interval ◽  
Point Boundary ◽  
At Resonance ◽  
The Given

This paper aims to investigate a class of fractional multi-point boundary value problems at resonance on an infinite interval. New existence results are obtained for the given problem using Mawhin’s coincidence degree theory. Moreover, two examples are given to illustrate the main results.

On Two-Point Boundary Value Problems for Two-Dimensional Differential Systems with Singularities

2003 ◽  
Vol 10 (3) ◽  
pp. 595-602
Author(s):  
S. Mukhigulashvili
Keyword(s):  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Differential System ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Continuous Functions ◽  
Two Dimensional ◽  
Point Boundary ◽  
Differential Systems

Abstract For a differential system where λ ∈]0, 1[ and ℎ𝑖 :]𝑎, 𝑏[×]0, +∞[×ℝ → [0, +∞[ (𝑖 = 0, 1, 2) are continuous functions, we have established sufficient conditions for the existence of at least one solution satisfying one of the two boundary conditions and

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