scholarly journals Existence of solution for a nonlinear fifth-order three-point boundary value problem

2019 ◽  
Vol 3 (2) ◽  
pp. 125-136 ◽  
Author(s):  
Zouaoui Bekri ◽  
◽  
Slimane Benaicha ◽  
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
Existence Of Solution ◽  
Point Boundary ◽  
Fifth Order

scholarly journals Existence of solution for nonlinear fourth-order three-point boundary value problem

2018 ◽  
Vol 38 (1) ◽  
pp. 67-82
Author(s):  
Zouaoui Bekri ◽  
Slimane Benaicha
Keyword(s):  
Boundary Value Problem ◽  
Nontrivial Solution ◽  
Fourth Order ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Existence Of Solution ◽  
Point Boundary ◽  
Nonlinear Alternative

In this paper, we study the existence of nontrivial solution for the fourth-order three- point boundary value problem having the following formu(4) (t) + f (t, u(t)) = 0, 0 < t < 1,u(0) = α(η), u'(0) = u''(0) = 0, u(1) = βu(η),where η ∈ (0, 1), α, β ∈ R, f ∈ C ([0, 1] × R, R). We give sufficient conditions that allow us to obtain the existence of a nontrivial solution. And by using the Leray-Schauder nonlinear alternative we prove the existence of at least one solution of the posed problem. As an application, we also given some examples to illustrate the results obtained.

scholarly journals On the existence of solution of a two-point boundary value problem in a cylindrical floating zone

2001 ◽  
Vol 25 (10) ◽  
pp. 669-677
Author(s):  
Shi Yongdong ◽  
Du Liangsheng
Keyword(s):  
Surface Tension ◽  
Boundary Value Problem ◽  
Solution Method ◽  
Boundary Value ◽  
Lower Solution ◽  
Existence Of Solution ◽  
Positive Parameter ◽  
Point Boundary ◽  
Floating Zone ◽  
Lower Solution Method

Existence of one solution for a two-point boundary value problem with a positive parameterQarising in the study of surface-tension-induced flows of a liquid metal or semiconductor is studied. On the basis of the upper-lower solution method and Schauder's fixed point theorem, it is proved that the problem admits a solution when0≤Q≤12.683. This improves a recent result where0≤Q<1.

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