Criteria of the three cases for non-self-adjoint singular Sturm-Liouville difference equations

References

• Atkinson , F.V. 1964 . Discrete and Continuous Boundary Value Problems , New York : Academic Press .
   Google Scholar
• Bennewitz , C. and Brown , B.M. 2002 . A limit point criterion with applications to non-self-adjoint equations . J. Comput. Appl. Math. , 148 : 257 – 265 .
   Web of Science ®Google Scholar
• Brown , B.M. , McCormack , D.K.R. , Evans , W.D. and Plum , M. 1999 . On the spectrum of second order differential operators with complex coefficients . Proc. R. Soc. Lond. A , 455 : 1235 – 1257 .
   Web of Science ®Google Scholar
• Brown , B.M. and Marletta , M. 2001 . Spectral inclusion and spectral exactness for singular non-self-adjoint Sturm-Liouville problems . Proc. R. Soc. Lond. A , 457 : 117 – 139 .
   Web of Science ®Google Scholar
• Brown , B.M. , Peacock , R.A. and Weikard , R. 2002 . A local Borg-Marchenko theorem for complex potentials . J. Comput. Appl. Math. , 148 : 115 – 131 .
   Web of Science ®Google Scholar
• Brown , B.M. and Marletta , M. 2003 . Spectral inclusion and spectral exactness for singular non-self-adjoint Hamiltonian systems . Proc. R. Soc. Lond. A , 459 : 1987 – 2009 .
   Web of Science ®Google Scholar
• Brown , B.M. , Evans , W.D. and Plum , M. 2003 . Titchmarsh–Sims–Weyl theory for complex Hamiltonian systems . Proc. Lond. Math. Soc. , 87 ( 2 ) : 419 – 450 .
   Web of Science ®Google Scholar
• Dunford , N. and Schwartz , J.T. 1963 . Linear Operators (II) , New York : Wiley-Interscience .
   Google Scholar
• Hille , E. 1969 . Lectures on Ordinary Differential Equations , London : Addison-Wesley .
   Google Scholar
• H. Jing, Deficiency index problem for singular non-symmetric Sturm-Liouville equations, MD thesis, Ningbo University
   Google Scholar
• Monaquel , S.J. and Schmidt , K.M. 2007 . On M-functions and operator theory for non-self-adjoint discrete Hamiltonian systems . J. Comput. Appl. Math. , 208 : 82 – 101 .
   Web of Science ®Google Scholar
• Qi , J. and Chen , S. 2004 . Strong limit-point classification of singular Hamiltonian expressions with complex coefficients . Proc. Amer. Math. Soc. , 132 : 1667 – 1674 .
   Web of Science ®Google Scholar
• Qi , J. 2005 . Non-limit-circle criteria for singular Hamiltonian differential systems . J. Math. Anal. Appl. , 305 : 599 – 616 .
   Web of Science ®Google Scholar
• Qi , J. and Zhou , S. 2005 . Limit-point criterion for singular linear Dirac differential systems . Comput. Math. Appl. , 49 : 765 – 775 .
   Web of Science ®Google Scholar
• Qi , J. 2007 . Limit-point criteria for semi-degenerate singular Hamiltonian differential systems with perturbation terms . J. Math. Anal. Appl. , 334 : 983 – 997 .
   Web of Science ®Google Scholar
• Sims , A.R. 1957 . Secondary conditions for linear differential operators of the second order . J. Math. Mech. , 6 ( 2 ) : 247 – 285 .
   Web of Science ®Google Scholar
• Shi , Y. 2006 . Weyl-Titchmarsh theory for a class of discrete linear Hamiltonian systems . Linear Algebra Appl. , 416 : 452 – 519 .
   Web of Science ®Google Scholar
• Sun , H. and Shi , Y. 2006 . Limit-point and limit-circle criteria for singular second-order linear difference equations with complex coefficients . Comput. Math. Appl. , 52 : 539 – 554 .
   Web of Science ®Google Scholar
• Sun , H. and Qi , J. 2010 . On classification of second-order differential equations with complex coefficients . J. Math. Anal. Appl. , 372 : 585 – 597 .
   Web of Science ®Google Scholar
• Sun , H. and Qi , J. 2011 . Classification of non-self-adjoint singular Sturm-Liouville difference equations . Appl. Math. Comput. , 217 : 8020 – 8030 .
   Web of Science ®Google Scholar
• Weidmann , J. 1987 . Spectral Theory of Ordinary Differential Operators , Lecture Notes in Mathematics Vol. 1258 , Berlin : Springer-Verlag .
   Google Scholar
• Weyl , H. 1910 . Über gewöhnliche Differentialgleichungen mit Singularitäten und die zugehörigen Entwicklungen willkürlicher Funktionen . Math. Ann. , 68 : 220 – 269 .
   Google Scholar
• Wilson , R.H. 2005 . Non-self-adjoint difference operators and their spectrum . Proc. R. Soc. A , 461 : 1505 – 1531 .
   Google Scholar