scholarly journals A note on the equivalence between even order Sturm–Liouville equations and symplectic systems on time scales

2013 ◽  
Vol 26 (1) ◽  
pp. 134-139 ◽  
Author(s):  
Petr Zemánek
Keyword(s):  
Time Scales ◽  
Even Order ◽  
Sturm Liouville

scholarly journals DUAL EQUATION AND INVERSE PROBLEM FOR AN INDEFINITE STURM–LIOUVILLE PROBLEM WITH M TURNING POINTS OF EVEN ORDER

2012 ◽  
Vol 17 (5) ◽  
pp. 618-629
Author(s):  
Hamidreza Marasi ◽  
Aliasghar Jodayree Akbarfam
Keyword(s):  
Inverse Problem ◽  
Infinite Product ◽  
Turning Points ◽  
Liouville Problem ◽  
Product Representation ◽  
Dual Equation ◽  
Number Of Zeros ◽  
Even Order ◽  
Sturm Liouville ◽  
Infinite Product Representation

In this paper the differential equation y″ + (ρ 2 φ 2 (x) –q(x))y = 0 is considered on a finite interval I, say I = [0, 1], where q is a positive sufficiently smooth function and ρ 2 is a real parameter. Also, [0, 1] contains a finite number of zeros of φ 2 , the so called turning points, 0 < x 1 < x 2 < … < x m < 1. First we obtain the infinite product representation of the solution. The product representation, satisfies in the original equation. As a result the associated dual equation is derived and then we proceed with the solution of the inverse problem.

Sturm-Liouville eigenvalue problems on time scales

1999 ◽  
Vol 99 (2-3) ◽  
pp. 153-166 ◽  
Author(s):  
Ravi P. Agarwal ◽  
Martin Bohner ◽  
Patricia J.Y. Wong
Keyword(s):  
Time Scales ◽  
Eigenvalue Problems ◽  
Sturm Liouville

Variable Change for Sturm-Liouville Differential Expressions on Time Scales

2003 ◽  
Vol 9 (1) ◽  
pp. 93-107
Author(s):  
Calvin Ahlbrandt ◽  
Martin Bohner ◽  
Tammy Voepel
Keyword(s):  
Time Scales ◽  
Sturm Liouville
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