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
Keyword(s):  
Boundary Value Problem ◽  
Time Scales ◽  
Fourth Order ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Point Boundary ◽  
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 Solvability of a nonlinear general third order four point eigenvalue problem on time scales

2011 ◽  
Vol 20 (2) ◽  
pp. 171-182
Author(s):  
S. NAGESWARA RAO ◽  
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Eigenvalue Problem ◽  
Boundary Value Problem ◽  
Time Scales ◽  
Boundary Value ◽  
Point Boundary ◽  
Third Order ◽  
Order Four

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.

scholarly journals Fourth-Order Four-Point Boundary Value Problem: A Solutions Funnel Approach

2012 ◽  
Vol 2012 ◽  
pp. 1-18
Author(s):  
Panos K. Palamides ◽  
Alex P. Palamides
Keyword(s):  
Vector Field ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Ordinary Differential Equations ◽  
Fourth Order ◽  
Boundary Value ◽  
Point Boundary ◽  
Negative Solution ◽  
Order Four ◽  
The Continuum

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.

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