Boundary-value problems for the third-order loaded equation with noncharacteristic type-change boundaries

2018 ◽  
Vol 41 (9) ◽  
pp. 3307-3315 ◽  
Author(s):  
Umida Baltaeva ◽  
Praveen Agarwal
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Third Order ◽  
The Third ◽  
Type Change ◽  
Loaded Equation

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.

Direct integration of the third-order two point and multipoint Robin type boundary value problems

2021 ◽  
Vol 182 ◽  
pp. 411-427
Author(s):  
Nadirah Mohd Nasir ◽  
Zanariah Abdul Majid ◽  
Fudziah Ismail ◽  
Norfifah Bachok
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Direct Integration ◽  
Third Order ◽  
The Third ◽  
Type Boundary

ON THE SOLUTIONS OF NONLINEAR THIRD ORDER BOUNDARY VALUE PROBLEMS

2010 ◽  
Vol 15 (1) ◽  
pp. 127-136
Author(s):  
Sergey Smirnov
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Order Equation ◽  
Structure Of Solutions ◽  
Third Order ◽  
Number Of Solutions ◽  
The Third

The author considers a three‐point third order boundary value problem. Properties and the structure of solutions of the third order equation are discussed. Also, a connection between the number of solutions of the boundary value problem and the structure of solutions of the equation is established.

Applications of the Method of Barriers II. Some Singularly Perturbed Problems

1995 ◽  
Vol 2 (3) ◽  
pp. 323-335
Author(s):  
V. G. Sushko ◽  
N. Kh. Rozov
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Singularly Perturbed ◽  
Point Boundary ◽  
Singularly Perturbed Problems ◽  
Quasilinear Equations ◽  
Third Order ◽  
The Third ◽  
Asymptotic Representations

Abstract The method of barriers is used to justify asymptotic representations of solutions of two-point boundary value problems for singularly perturbed quasilinear equations of the second and the third order. This paper is a continuation of [Rozov and Sushko, Georgian Math. J. 2: 99-110, 1995].

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 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 On the Uniqueness Classes of Solutions of Boundary Value Problems for Third-Order Equations of the Pseudo-Elliptic Type

Axioms ◽  
2020 ◽  
Vol 9 (3) ◽  
pp. 80
Author(s):  
Abdukomil Risbekovich Khashimov ◽  
Dana Smetanová
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
The Body ◽  
Energy Estimates ◽  
Uniqueness Theorems ◽  
Elliptic Type ◽  
Third Order ◽  
Body Form ◽  
The Third

The paper is devoted to solutions of the third order pseudo-elliptic type equations. An energy estimates for solutions of the equations considering transformation’s character of the body form were established by using of an analog of the Saint-Venant principle. In consequence of this estimate, the uniqueness theorems were obtained for solutions of the first boundary value problem for third order equations in unlimited domains. The energy estimates are illustrated on two examples.

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