A representation for solutions of the Sturm–Liouville equation

Complex Variables and Elliptic Equations

Volumn 53, Issue 8, 2008, Pages 775-789

  Kravchenko, Vladislav V ^a  

^a DEPARTAMENTO DE FÍSICA   (Mexico)

Author keywords

30G20; 34B24; 34L16; 81Q60; Darboux transformation; pseudoanalytic functions; Schr dinger equation; Sturm Liouville problem; Vekua equation

Indexed keywords

EID: 54049146843     PISSN: 17476933     EISSN: 17476941     Source Type: Journal    
DOI: 10.1080/17476930802102894     Document Type: Article

References (12)

1. Demidenko, E. 2006. Separable Laplace equation, magic Toeplitz matrix, and generalized Ohm's law. App. Math. Comput., 181: 1313–1327.
2. Chadan, K and Kobayashi, R. 2006. New classes of potentials for which the radial Schrödinger equation can be solved at zero energy. J. Phys. A: Math. Gen., 39: 3381–3396.
3. 2006. New classes of potentials for which the radial Schrödinger equation can be solved at zero energy: II. J. Phys. A: Math. Gen., 39: 13691–13699.
4. Bers, L. 1952. Theory of Pseudo-Analytic Functions, New York: New York University.
5. Kravchenko, VV. 2005. On a relation of pseudoanalytic function theory to the two-dimensional stationary Schrödinger equation and Taylor series in formal powers for its solutions. J. Phys. A: Math. Gen., 38: 3947–3964.
6. 2006. On a factorization of second order elliptic operators and applications. J. Phys. A: Math. Gen., 39: 12407–12425.
7. Escassut, A, Tutschke, W and Yang, CC, eds. 2008. “ Recent developments in applied pseudoanalytic function theory ”. In Some Topics on Value Distribution and Differentiability in Complex and p-adic Analysis, 267–300. Beijing: Science Press.
8. Levitan, BM and Sargsjan, IS. 1991. Sturm–Liouville and Dirac Operators, Dordrecht: Kluwer Academic Publishers.
9. Zettl, A. 1997. “ Sturm–Liouville problems ”. In Spectral Theory and Computational Methods of Sturm–Liouville Problems (Knoxville, TN, 1996), Lecture Notes in Pure and Applied Mathematics Edited by: Hinton, D and Schaefer, PW. Vol. 191, 1–104. New York: Dekker.
10. Pöschel, J and Trubowitz, E. 1987. Inverse Spectral Theory, Boston: Academic Press.
11. Matveev, V and Salle, M. 1991. Darboux Transformations and Solitons, New York: Springer.
12. Vekua, IN. 1962. Generalized Analytic Functions, Oxford: English translation, Pergamon Press. Nauka, Moscow, 1959 (in Russian)