scholarly journals Existence of Solutions for Fourth-Order Four-Point Boundary Value Problem on Time Scales

2009 ◽  
Vol 2009 ◽  
pp. 1-20
Author(s):  
Dandan Yang ◽  
Gang Li ◽  
Chuanzhi Bai
2012 ◽  
Vol 2012 ◽  
pp. 1-14
Author(s):  
Ilkay Yaslan Karaca

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.


2011 ◽  
Vol 20 (2) ◽  
pp. 171-182
Author(s):  
S. NAGESWARA RAO ◽  

We consider the four point boundary value problem for third order nonlinear differential equation on time scales ... subject to the boundary conditions ... t1 ≤ t2 ≤ t3 ≤ σ 3 (t4), α > 0, β > 0. Values of the parameter λ are determined for which the boundary value problem has a positive solution by utilizing a fixed point theorem on cone.


2012 ◽  
Vol 2012 ◽  
pp. 1-18
Author(s):  
Panos K. Palamides ◽  
Alex P. Palamides

We investigate the existence of positive or a negative solution of several classes of four-point boundary-value problems for fourth-order ordinary differential equations. Although these problems do not always admit a (positive) Green's function, the obtained solution is still of definite sign. Furthermore, we prove the existence of an entire continuum of solutions. Our technique relies on the continuum property (connectedness and compactness) of the solutions funnel (Kneser's Theorem), combined with the corresponding vector field.


Sign in / Sign up

Export Citation Format

Share Document