Stability of solutions to Sturm-Liouville diffusion equations

References

• Case , K. M. and Zweifel , P. F. 1967 . “Linear Transport Theory” , Reading, Mass. : Addison-Wesley .
   Google Scholar
• Sobolev , V. V. 1975 . “Light Scattering in Planetary Atmospheres” , London : Pergamon Press .
   Google Scholar
• Chandrasekhar , S. 1973 . Rev. Mod. Phys. , 15 : 1
   Google Scholar
• van der Mee , C. V.M. 1982 . Int. Eqs. Oper. Theor. , 5 : 573
   Google Scholar
• Feldman , I. A. 1975 . Matem. Issled. Kishinev , 10 ( 3 ) : 226
   Google Scholar
• Ran , A. C.M. and Rodman , L. 1985 . Int. Eqs. Oper. Theor. , 8 : 75
   Google Scholar
• Hangelbroek , R. J. 1985 . Int. Eqs. Oper. Theor. , 8 : 1
   Google Scholar
• Beals , R. 1979 . J. Funct. Anal. , 34 : 1
   Web of Science ®Google Scholar
• Hangelbroek , R. J. 1976 . Transp. Theor. Stat. Phys. , 5 : 1
   Web of Science ®Google Scholar
• Lekkerkerker , C. G. 1976 . Proc. Edinburgh Math. Soc. , 75A : 283
   Web of Science ®Google Scholar
• van der Mee , C. V.M. 1981 . “Semigroup and Factorization Methods in Transport Theory” . Math. Centre Tract , 146 Amsterdam
   Google Scholar
• Greenberg , W. , van der Mee , C. V.M. and Zweifel , P. F. 1984 . Int. Eqs. Oper. Theor. , 7 : 60
   Google Scholar
• Beals , R. 1985 . J. Diff. Eqs. , 56 : 391
   Web of Science ®Google Scholar
• Berezanskii , Yu. M. 1968 . “Expansions in Eigenfunctions of Self-Adjoint Operators” , Providence, R. I. : A.M.S. . Transl. Math. Monographs 17 Theorem I 1.2.
   Google Scholar
• Krein , M. G. 1947 . Akad. Nauk Ukrain. SSR, Zbirnik Prats Inst. Mat. , 9 : 104 Theorem 1. Original result by
   Google Scholar
• Kato , T. 1966 . “Perturbation Theory for Linear Operators” , Berlin : Springer .
   Google Scholar
• Greenberg , W. and van der Mee , C. V.M. 1984 . Z. Angew. Math. Phys. , 35 : 156 Here abstract half-space theory is developed using vanishing solutions for x Similar methods can be used for the problem studied in Ref. [13] to obtain half-space existence or non-existence results for solutions vanishing at infinity
   Web of Science ®Google Scholar
• Bart , H. , Gohberg , I. and Kaashoek , M. A. 1979 . “Minimal Factorization of Matrix and Operator Functions” , Vol. 1 , Basel, OT : Birkhäuser .
   Google Scholar
• Hille , E. 1969 . “Lectures on Ordinary Differential Equations” , London : Addison-Wesley .
   Google Scholar
• Coddington , E. A. and Levinson , N. 1955 . “Theory of Ordinary Differential Equations” , New York : McGraw-Hill .
   Google Scholar
• Bothe , W. 1929 . Z. Phys. , 54 : 161
   Google Scholar
• Everitt , W. N. “Legendre Polynomials and Singular Differential Operators” . Proceedings Dundee Conference . 1978 . Edited by: Everitt , W. N. pp. 827 Berlin : Springer . Lecture Notes in Mathematics
   Google Scholar
• It should be noted that this result also appeared in the below Ref. [24]. The proof in this publication is incomplete, since the authors restricted themselves to proving the unique solvability of an auxiliary half-space problem of the type (2.14)-(2.16) without subsequently matching the boundary conditions of the original half-space problem
   Google Scholar
• Beals , R. and Protopopescu , V. 1983 . J. Stat. Phys. , 32 : 565
   Web of Science ®Google Scholar
• Kaper , H. G. , Kwong , M. K. , Lekkerkerker , C. G. and Zettl , A. 1984 . Proc. Edinburgh Math. Soc. , 98A : 69
   Google Scholar