Transformations and the number of focal points for conjoined bases of symplectic difference systems

References

• Ahlbrandt , C.D. , Hinton , D.B. and Lewis , R.T. 1981 . The effect of variable change on oscillation and disconjugacy criteria with applications to spectral theory and asymptotic theory . J. Math. Anal. Appl. , 81 : 234 – 277 .
   Web of Science ®Google Scholar
• Ahlbrandt , C.D. and Peterson , A. 1994 . The (n,n) -disconjugacy of a 2nth order linear difference equation . Comput. Math. Appl. , 28 : 1 – 9 .
   Web of Science ®Google Scholar
• Bohner , M. 1996 . Linear Hamiltonian difference systems: disconjugacy and Jacobi-type conditions . J. Math. Anal. Appl. , 199 : 804 – 826 .
   Web of Science ®Google Scholar
• Bohner , M. 1997 . Symplectic systems and related discrete quadratic functionals . Facta Univ. Ser. Math. Inform. , 12 : 143 – 156 .
   Google Scholar
• Bohner , M. 1998 . Discrete Sturmian theory . Math. Inequal. Appl. , 1 : 375 – 383 .
   Web of Science ®Google Scholar
• Bohner , M. and Došlý , O. 1997 . Disconjugacy and transformations for symplectic systems . Rocky Mountain J. Math. , 27 : 707 – 743 .
   Web of Science ®Google Scholar
• Bohner , M. and Došlý , O. 2000 . Trigonometric transformations of symplectic difference systems . J. Differential Equations , 163 : 113 – 129 .
   Google Scholar
• Bohner , M. and Došlý , O. 2004 . Oscillation of symplectic dynamic systems . ANZIAM J. , 46 : 17 – 32 .
   Google Scholar
• Bohner , M. , Došlý , O. and Kratz , W. 1999 . A Sturmian theorem for recessive solutions of linear Hamiltonian difference systems . Appl. Math. Lett. , 12 : 101 – 106 .
   Web of Science ®Google Scholar
• Bohner , M. , Došlý , O. and Kratz , W. 2003 . An oscillation theorem for discrete eigenvalue problems . Rocky Mountain J. Math. , 33 : 1233 – 1260 .
   Web of Science ®Google Scholar
• M. Bohner, O. Došlý, and W. Kratz, Sturmian and spectral theory for discrete symplectic systems, Trans. Amer. Math. Soc. 361 (2009), pp. 3109–3123
   Google Scholar
• Coppel , W.A. 1971 . “ Disconjugacy ” . In Lect. Notes Math. , 220 New York : Springer . 220
   Google Scholar
• Došlý , O. 1991 . Transformations of linear Hamiltonian systems preserving oscillatory behaviour . Arch. Math. (Brno) , 27b : 211 – 219 .
   Google Scholar
• Došlý , O. and Hilscher , R. 1999 . Linear Hamiltonian difference systems: transformations, recessive solutions, generalized reciprocity . Dynam. Systems Appl. , 8 : 401 – 420 .
   Google Scholar
• Dosly , O. and Kratz , W. 2007 . Oscillation theorems for symplectic difference systems . J. Difference Equ. Appl. , 13 : 585 – 605 .
   Web of Science ®Google Scholar
• Elyseeva , J. 2007 . “ The comparative index for conjoined bases of symplectic difference systems ” . In Difference Equations, Special Functions and Orthogonal Polynomials , 168 – 177 . Singapore : World Scientific . Munich, Germany, 25–30 July 2005
   Google Scholar
• J. Elyseeva, The comparative index for solutions of symplectic difference systems, Differ. Equ. (2009), to appear
   Google Scholar
• Erbe , L. and Yan , P. 1992 . Disconjugacy for linear Hamiltonian difference systems . J. Math. Anal. Appl. , 167 : 355 – 367 .
   Web of Science ®Google Scholar
• R. Hilscher and V. Zeidan, Multiplicities of focal points for discrete symplectic systems: revisited, J. Difference Equ. Appl. (2009), to appear
   Google Scholar
• Kratz , W. 2003 . Discrete oscillation . J. Difference Equ. Appl. , 9 : 135 – 147 .
   Web of Science ®Google Scholar
• Rasmussen , C.H. 1979 . Oscillation and asymptotic behaviour of systems of ordinary linear differential equations . Trans. Amer. Math. Soc. , 256 : 1 – 49 .
   Web of Science ®Google Scholar
• Reid , W.T. 1980 . Sturmian Theory for Ordinary Differential Equations , New York : Springer .
   Google Scholar