scholarly journals On the isomonodromic deformation of a linear ordinary differential equation of the third order

1983 ◽  
Vol 59 (6) ◽  
pp. 219-222
Author(s):  
Hironobu Kimura
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Linear Ordinary Differential Equation ◽  
Isomonodromic Deformation ◽  
Third Order ◽  
The Third

Construction of Green’s functional for a third order ordinary differential equation with general nonlocal conditions and variable principal coefficient

2020 ◽  
Vol 27 (4) ◽  
pp. 593-603 ◽  
Author(s):  
Kemal Özen
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Nonlocal Problem ◽  
Nonlocal Conditions ◽  
Adjoint Problem ◽  
Linear Ordinary Differential Equation ◽  
Third Order ◽  
Order Ordinary Differential Equation ◽  
Order Linear ◽  
Theoretical Results

AbstractIn this work, the solvability of a generally nonlocal problem is investigated for a third order linear ordinary differential equation with variable principal coefficient. A novel adjoint problem and Green’s functional are constructed for a completely nonhomogeneous problem. Several illustrative applications for the theoretical results are provided.

A System Associated with the Confluent Hypergeometric Function Φ3 and a Certain Linear Ordinary Differential Equation with Two Irregular Singular Points

1997 ◽  
Vol 08 (05) ◽  
pp. 689-702 ◽  
Author(s):  
Shun Shimomura
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Hypergeometric Function ◽  
Confluent Hypergeometric Function ◽  
Linear Ordinary Differential Equation ◽  
Singular Points ◽  
Third Order ◽  
Regular Type ◽  
Singular Loci ◽  
Irregular Singular Points

The confluent hypergeometric function Φ3 satisfies a system of partial differential equations on P1(C) × P1(C) with the singular loci x = 0, x = ∞, y = ∞ of irregular type and y = 0 of regular type. We obtain asymptotic expansions and Stokes multipliers of linearly independent solutions near the singular loci x = 0 and x = ∞. Applying the results we also clarify the global behaviour of the solutions of a third order linear ordinary differential equation with two irregular singular points.

scholarly journals Classroom Note: Numerical solutions of Nagumo's equation

1999 ◽  
Vol 3 (2) ◽  
pp. 189-193 ◽  
Author(s):  
M. Iqbal
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Numerical Solutions ◽  
Linear Ordinary Differential Equation ◽  
Bounded Solutions ◽  
Third Order ◽  
Non Linear

Nagumo's equation is a third order non-linear ordinary differential equation d3udx3−cd2udx2+f′(u)dudx−(b/c)u=0 where f(u)=u(1−u)(u−α) , 0<α<1 . In this paper we have developed a technique to determine those values of the parameters a,b and c which permit non-constant bounded solutions.

scholarly journals On the third order boundary value problems with asymmetric nonlinearity

2011 ◽  
Vol 16 (2) ◽  
pp. 231-241 ◽  
Author(s):  
Sergey Smirnov
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Third Order ◽  
Number Of Solutions ◽  
The Third ◽  
Asymmetric Nonlinearity ◽  
Autonomous Ordinary Differential Equation

The author considers two point third order boundary value problem with asymmetric nonlinearity. The structure and oscillatory properties of solutions of the third order nonlinear autonomous ordinary differential equation are discussed. Results on the estimation of the number of solutions to boundary value problem are provided. An illustrative example is given.

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.

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.

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