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

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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ON THE SOLUTIONS OF NONLINEAR THIRD ORDER BOUNDARY VALUE PROBLEMS

Mathematical Modelling and Analysis ◽

10.3846/1392-6292.2010.15.127-136 ◽

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.

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On the third order boundary value problems with asymmetric nonlinearity

Nonlinear Analysis Modelling and Control ◽

10.15388/na.16.2.14108 ◽

2011 ◽

Vol 16 (2) ◽

pp. 231-241 ◽

Cited By ~ 2

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.

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Existence and uniqueness theorems for a third-order generalized boundary value problem

Journal of Applied Mathematics and Simulation ◽

10.1155/s1048953389000031 ◽

1989 ◽

Vol 2 (1) ◽

pp. 33-51

Author(s):

Chaitan P. Gupta

Keyword(s):

Boundary Value Problem ◽

Existence And Uniqueness ◽

Boundary Value ◽

Uniqueness Theorems ◽

Linear Boundary ◽

Third Order ◽

The Third ◽

Special Cases ◽

Linear Boundary Value Problem ◽

Natural Way

Let f:[0,1]×ℝ3→ℝ be a function satisfying Caratheodory's conditions, e(x)∈L1[0,1], η∈[0,1], h≥0, k≥0, h+k>0. This paper studies existence and uniqueness questions for the third-order three-point generalized boundary value problem u‴+f(x,u,u′,u″)=e(x), 0<x<1, u(η)=0, u″(0)−hu′(0)=u″(1)+ku′(1)=0, and the associated special cases corresponding to one or both of h and k equal to infinity. The conditions on the nonlinearity f turn out to be related to the spectrum of the linear boundary value problem u‴=λu′, u(η)=0, u″(0)−hu′(0)=u″(1)+ku′(1)=0, in a natural way.

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

Proceedings of the Edinburgh Mathematical Society ◽

10.1017/s0013091514000042 ◽

2014 ◽

Vol 58 (1) ◽

pp. 183-197 ◽

Cited By ~ 2

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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