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.

Oscillation criteria for third-order nonlinear differential equations

2008 ◽  
Vol 58 (2) ◽  
Author(s):  
B. Baculíková ◽  
E. Elabbasy ◽  
S. Saker ◽  
J. Džurina
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Order Differential Equation ◽  
Nonlinear Differential Equations ◽  
Sufficient Conditions ◽  
Third Order ◽  
Oscillation Criteria ◽  
The Third ◽  
Third Order Differential Equation ◽  
Oscillation Properties

AbstractIn this paper, we are concerned with the oscillation properties of the third order differential equation $$ \left( {b(t) \left( {[a(t)x'(t)'} \right)^\gamma } \right)^\prime + q(t)x^\gamma (t) = 0, \gamma > 0 $$. Some new sufficient conditions which insure that every solution oscillates or converges to zero are established. The obtained results extend the results known in the literature for γ = 1. Some examples are considered to illustrate our main results.

scholarly journals Optimality and existence for Lipschitz equations

1988 ◽  
Vol 11 (2) ◽  
pp. 267-274
Author(s):  
Johnny Henderson
Keyword(s):  
Differential Equation ◽  
Boundary Value Problems ◽  
Lipschitz Condition ◽  
Order Differential Equation ◽  
Boundary Value ◽  
Optimal Length

Solutions of certain boundary value problems are shown to exist for thenth order differential equationy(n)=f(t,y,y′,…,y(n−1)), wherefis continuous on a slab(a,b)×Rnandfsatisfies a Lipschitz condition on the slab. Optimal length subintervals of(a,b)are determined, in terms of the Lipschitz coefficients, on which there exist unique solutions.

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