scholarly journals Upper and lower solution method for fourth-order four-point boundary value problems

2009 ◽  
Vol 223 (2) ◽  
pp. 543-551 ◽  
Author(s):  
De-xiang Ma ◽  
Xiao-zhong Yang
Keyword(s):  
Boundary Value Problems ◽  
Fourth Order ◽  
Solution Method ◽  
Boundary Value ◽  
Lower Solution ◽  
Point Boundary ◽  
Upper And Lower Solution ◽  
Lower Solution Method ◽  
Order Four

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 Existence of Solutions of Nonlinear Mixed Two-Point Boundary Value Problems for Third-Order Nonlinear Differential Equation

2012 ◽  
Vol 2012 ◽  
pp. 1-12
Author(s):  
Yongxin Gao ◽  
Fengqin Wang
Keyword(s):  
Differential Equation ◽  
Boundary Value Problems ◽  
Nonlinear Differential Equation ◽  
Solution Method ◽  
Existence Of Solutions ◽  
Lower Solution ◽  
Point Boundary ◽  
Third Order ◽  
Upper And Lower Solution ◽  
Lower Solution Method

The authors use the upper and lower solution method to study the existence of solutions of nonlinear mixed two-point boundary value problems for third-order nonlinear differential equation  y′′′=f(x,y,y′,y′′),  y′(b)=h(y′(a)),  p(y(a),y(b),y′(a),y′(b))=0,  g(y(a),y(b),y′(a),y′(b),y′′(a),y′′(b))=0. Some new existence results are obtained by developing the upper and lower solution method. Some applications are also presented.

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