scholarly journals Upper and Lower Solution Method for Fourth-Order Four-Point Boundary Value Problem on Time Scales

2012 ◽  
Vol 2012 ◽  
pp. 1-14
Author(s):  
Ilkay Yaslan Karaca
Keyword(s):  
Boundary Value Problem ◽  
Time Scales ◽  
Fourth Order ◽  
Solution Method ◽  
Boundary Value ◽  
Lower Solution ◽  
Point Boundary ◽  
Upper And Lower Solution ◽  
Lower Solution Method ◽  
Order Four

We consider a fourth-order four-point boundary value problem for dynamic equations on time scales. By the upper and lower solution method, some results on the existence of solutions of the fourth-order four-point boundary value problem on time scales are obtained. An example is also included to illustrate our results.

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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