scholarly journals Existence Theory for Nonlinear Third-Order Ordinary Differential Equations with Nonlocal Multi-Point and Multi-Strip Boundary Conditions

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 281 ◽  
Author(s):  
Ahmed Alsaedi ◽  
Mona Alsulami ◽  
Hari Srivastava ◽  
Bashir Ahmad ◽  
Sotiris Ntouyas
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Existence Theory ◽  
Ulam Stability ◽  
Point Boundary ◽  
Arbitrary Domain ◽  
Third Order ◽  
Order Ordinary Differential Equation ◽  
The Third ◽  
Nonlocal Nonlinear

We investigate the solvability and Ulam stability for a nonlocal nonlinear third-order integro-multi-point boundary value problem on an arbitrary domain. The nonlinearity in the third-order ordinary differential equation involves the unknown function together with its first- and second-order derivatives. Our main results rely on the modern tools of functional analysis and are well illustrated with the aid of examples. An analogue problem involving non-separated integro-multi-point boundary conditions is also discussed.

Boundary-Value Problems for Third-Order Lipschitz Ordinary Differential Equations

2014 ◽  
Vol 58 (1) ◽  
pp. 183-197 ◽  
Author(s):  
John R. Graef ◽  
Johnny Henderson ◽  
Rodrica Luca ◽  
Yu Tian
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Boundary Value Problems ◽  
Order Differential Equation ◽  
Boundary Value ◽  
Point Boundary ◽  
Third Order ◽  
Optimal Length ◽  
The Third

AbstractFor the third-order differential equationy′″ = ƒ(t, y, y′, y″), where, questions involving ‘uniqueness implies uniqueness’, ‘uniqueness implies existence’ and ‘optimal length subintervals of (a, b) on which solutions are unique’ are studied for a class of two-point boundary-value problems.

Third-order differential equations with three-point boundary conditions

2021 ◽  
Vol 19 (1) ◽  
pp. 11-31
Author(s):  
Alberto Cabada ◽  
Nikolay D. Dimitrov
Keyword(s):  
Boundary Conditions ◽  
Fixed Point Theorems ◽  
Nonnegative Function ◽  
Time Dependent ◽  
Point Boundary ◽  
Positive Real ◽  
Third Order ◽  
Order Ordinary Differential Equation ◽  
Positive Real Parameter ◽  
Increasing Functions

Abstract In this paper, a third-order ordinary differential equation coupled to three-point boundary conditions is considered. The related Green’s function changes its sign on the square of definition. Despite this, we are able to deduce the existence of positive and increasing functions on the whole interval of definition, which are convex in a given subinterval. The nonlinear considered problem consists on the product of a positive real parameter, a nonnegative function that depends on the spatial variable and a time dependent function, with negative sign on the first part of the interval and positive on the second one. The results hold by means of fixed point theorems on suitable cones.

Finite Difference Method for a Second-order Ordinary Differential Equation with a Boundary Condition of the Third Kind

2010 ◽  
Vol 10 (1) ◽  
pp. 109-116 ◽  
Author(s):  
P.K. Pandey
Keyword(s):  
Differential Equation ◽  
Boundary Condition ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Second Order ◽  
Point Boundary ◽  
Order Ordinary Differential Equation ◽  
Numerical Examples ◽  
The Third

Abstract We present a second-order finite difference method for obtaining a solution of a second order two-point boundary value problem subject to Sturm's boundary conditions. We use equidistant discretization points, and the discretization of the differential equation at an interior point is based on just two evaluations of the function. Numerical examples are considered and the convergence of the proposed method is proved computationally.

The spectral representation of two-point boundary-value problems for third-order linear evolution partial differential equations

2005 ◽  
Vol 461 (2061) ◽  
pp. 2965-2984 ◽  
Author(s):  
Beatrice Pelloni
Keyword(s):  
Integral Representation ◽  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Series Representation ◽  
Point Boundary ◽  
Third Order ◽  
Linear Evolution ◽  
The Third ◽  
Order Case

We use a spectral transform method to study general boundary-value problems for third-order, linear, evolution partial differential equations with constant coefficients, posed on a finite space domain. We show how this method yields a simple characterization of the discrete spectrum of the associated spatial differential operator, and discuss the obstructions that arise when trying to represent the solution of such a problem as a series of exponential functions. We first review the theory for second-order two-point boundary-value problems, and present an alternative way to derive the classical series representation, as well as an equivalent integral representation, which generally involves complex contours. We illustrate the advantages of the integral representation by studying in some detail the case where Robin-type boundary conditions are prescribed. We then consider the third-order case and show that the integral representation is in general not equivalent to a discrete series representation, justifying a posteriori the failure of some of the classical approaches. We illustrate the third-order case in detail, using the example of the equation q t + q xxx =0 for various types of boundary conditions. In contrast with the second-order case, the qualitative properties of the spectrum of the associated spatial differential operator depend in this case not only on the equation but also on the type of boundary conditions. In particular, the solution appears to admit a series representation only when the prescribed boundary conditions couple the two endpoints of the interval.

scholarly journals Linearizability of Nonlinear Third-Order Ordinary Differential Equations by Using a Generalized Linearizing Transformation

2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
E. Thailert ◽  
S. Suksern
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Differential Equations ◽  
Linear Equation ◽  
Ordinary Differential Equations ◽  
Third Order ◽  
Order Ordinary Differential Equation ◽  
The Third ◽  
Linearization Problem ◽  
Linearizable Equation

We discuss the linearization problem of third-order ordinary differential equation under the generalized linearizing transformation. We identify the form of the linearizable equations and the conditions which allow the third-order ordinary differential equation to be transformed into the simplest linear equation. We also illustrate how to construct the generalized linearizing transformation. Some examples of linearizable equation are provided to demonstrate our procedure.

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