scholarly journals On nonlinear discontinuous two-point boundary value problems for third order differential equations

Filomat ◽  
2007 ◽  
Vol 21 (2) ◽  
pp. 185-197
Author(s):  
M.S.N. Murty ◽  
Suresh Kumar
Keyword(s):  
Differential Equations ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Extremal Solutions ◽  
Differential Inequalities ◽  
Point Boundary ◽  
Uniqueness Of Solutions ◽  
Third Order

In this paper we prove existence of weak extremal solutions for third order nonlinear discontinuous two-point boundary value problems. Further, we obtain two weak differential inequalities for proving boundedness and uniqueness of solutions of related boundary value problems. .

scholarly journals THEORY OF DIFFERENTIAL INEQUALITIES ASSOCIATED WITH $n$th ORDER NONLINEAR DIFFERENTIAL EQUATIONS AND THEIR APPLICATIONS TO THREE POINT BOUNDARY VALUE PROBLEMS

1998 ◽  
Vol 29 (2) ◽  
pp. 137-144
Author(s):  
K. N. MURTHY ◽  
C. V. RAO
Keyword(s):  
Differential Equations ◽  
Boundary Value Problems ◽  
Nonlinear Differential Equations ◽  
Boundary Value ◽  
Differential Inequalities ◽  
Point Boundary ◽  
Uniqueness Of Solutions

Differential inequalities are used as a tool to establish uniqueness of solutions to three point boundary value problems associated with nth order nonlinear differential equations.

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.

scholarly journals A note on solvability of three-point bound-ary value problems for third-order differential equations with p-Laplacian

2008 ◽  
Vol 39 (1) ◽  
pp. 95-103
Author(s):  
XingYuan Liu ◽  
Yuji Liu
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Boundary Value Problems ◽  
Order Differential Equation ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Point Boundary ◽  
Third Order ◽  
Third Order Differential Equation

Third-point boundary value problems for third-order differential equation$ \begin{cases} & [q(t)\phi(x''(t))]'+kx'(t)+g(t,x(t),x'(t))=p(t),\;\;t\in (0,1),\\ &x'(0)=x'(1)=x(\eta)=0. \end{cases} $is considered. Sufficient conditions for the existence of at least one solution of above problem are established. Some known results are improved.

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