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Volumn 45, Issue 3, 2002, Pages 631-645

Sturm-Liouville problems with boundary conditions rationally dependent on the eigenparameter. I

Author keywords

Eigenfunction oscillation; Eigenparameter dependent boundary condition; Eigenvalue asymptotics; Sturm Liouville

Indexed keywords


EID: 0036803328     PISSN: 00130915     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0013091501000773     Document Type: Conference Paper
Times cited : (70)

References (27)
  • 1
    • 0011197976 scopus 로고
    • A modification of Crum's method
    • V.È. Adler, A modification of Crum's method, Theor. Math. Phys. 101 (1994), 1381-1386.
    • (1994) Theor. Math. Phys. , vol.101 , pp. 1381-1386
    • Adler, V.È.1
  • 3
    • 0002218576 scopus 로고
    • On Sturm-Liouville problems with the square root of the eigenvalue parameter contained in the boundary conditions
    • A.I. Benedek and R. Panzone, On Sturm-Liouville problems with the square root of the eigenvalue parameter contained in the boundary conditions, Notas Algebra Analysis 10 (1981), 1-62.
    • (1981) Notas Algebra Analysis , vol.10 , pp. 1-62
    • Benedek, A.I.1    Panzone, R.2
  • 4
    • 84974183631 scopus 로고
    • Sturm-Liouville problems with eigen-parameter dependent boundary conditions
    • P.A. Binding, P.J. Browne and K. Seddighi, Sturm-Liouville problems with eigen-parameter dependent boundary conditions, Proc. Edinb. Math. Soc. 37 (1993), 57-72.
    • (1993) Proc. Edinb. Math. Soc. , vol.37 , pp. 57-72
    • Binding, P.A.1    Browne, P.J.2    Seddighi, K.3
  • 5
    • 0035920098 scopus 로고    scopus 로고
    • Elliptic eigenvalue problems with eigenparameter dependent boundary conditions
    • P.A. Binding, R. Hryniv, H. Langer and B. Najman, Elliptic eigenvalue problems with eigenparameter dependent boundary conditions, J. Diff. Eqns 174 (2001), 30-54.
    • (2001) J. Diff. Eqns , vol.174 , pp. 30-54
    • Binding, P.A.1    Hryniv, R.2    Langer, H.3    Najman, B.4
  • 6
    • 0035516009 scopus 로고    scopus 로고
    • Transformations between Sturm-Liouville problems with eigenvalue dependent and independent boundary conditions
    • P.A. Binding, P.J. Browne and B.A. Watson, Transformations between Sturm-Liouville problems with eigenvalue dependent and independent boundary conditions, Bull. Lond. Math. Soc. 33 (2001), 749-757.
    • (2001) Bull. Lond. Math. Soc. , vol.33 , pp. 749-757
    • Binding, P.A.1    Browne, P.J.2    Watson, B.A.3
  • 7
    • 0242323275 scopus 로고
    • Associated Sturm-Liouville systems
    • M.M. Crum, Associated Sturm-Liouville systems, Q. J. Math. 6 (1955), 121-127.
    • (1955) Q. J. Math. , vol.6 , pp. 121-127
    • Crum, M.M.1
  • 8
    • 84972582239 scopus 로고
    • Applications of a commutation formula
    • P. Deift, Applications of a commutation formula, Duke Math. J. 45 (1978), 267-310.
    • (1978) Duke Math. J. , vol.45 , pp. 267-310
    • Deift, P.1
  • 9
    • 84971109156 scopus 로고
    • Eigenfunction expansions for a class of J-selfadjoint ordinary differential operators with boundary conditions containing the eigenvalue parameter
    • A. Dijksma, Eigenfunction expansions for a class of J-selfadjoint ordinary differential operators with boundary conditions containing the eigenvalue parameter, Proc. R. Soc. Edinb. A 86 (1980), 1-27.
    • (1980) Proc. R. Soc. Edinb. A , vol.86 , pp. 1-27
    • Dijksma, A.1
  • 10
    • 0001917037 scopus 로고    scopus 로고
    • Operator theory and ordinary differential operators
    • A. Dijksma and H. Langer, Operator theory and ordinary differential operators, Fields Inst. Monographs 3 (1996), 75-139.
    • (1996) Fields Inst. Monographs , vol.3 , pp. 75-139
    • Dijksma, A.1    Langer, H.2
  • 11
    • 0002966304 scopus 로고
    • Symmetric Sturm-Liouville operators with eigenvalue depending boundary conditions
    • A. Dijksma, H. Langer and H. De Snoo, Symmetric Sturm-Liouville operators with eigenvalue depending boundary conditions, Can. Math. Soc. Conf. Proc. 8 (1987), 87-116.
    • (1987) Can. Math. Soc. Conf. Proc. , vol.8 , pp. 87-116
    • Dijksma, A.1    Langer, H.2    De Snoo, H.3
  • 12
    • 0011167293 scopus 로고
    • Note on a paper of E.M.E. Zayed and S.F.M. Ibrahim: 'Eigenfunction expansion for a regular fourth order eigenvalue problem with eigenvalue parameter in the boundary conditions'
    • Int. J. Math. Math. Sci. 12 (1989), 341-348; MR 90h:34043
    • W. Eberhard, G. Freiling and A. Schneider, Note on a paper of E.M.E. Zayed and S.F.M. Ibrahim: 'Eigenfunction expansion for a regular fourth order eigenvalue problem with eigenvalue parameter in the boundary conditions' [Int. J. Math. Math. Sci. 12 (1989), 341-348; MR 90h:34043], Int. J. Math. Math. Sci. 15 (1992), 809-811.
    • (1992) Int. J. Math. Math. Sci. , vol.15 , pp. 809-811
    • Eberhard, W.1    Freiling, G.2    Schneider, A.3
  • 13
    • 0002481002 scopus 로고
    • Some boundary value problems with a spectral parameter in the boundary conditions
    • A.E. Ètkin, Some boundary value problems with a spectral parameter in the boundary conditions, Am. Math. Soc. Transl. 2 136 (1987), 35-41.
    • (1987) Am. Math. Soc. Transl. 2 , vol.136 , pp. 35-41
    • Ètkin, A.E.1
  • 14
    • 84971166919 scopus 로고
    • Two-point boundary value problems with eigenvalue parameter contained in the boundary conditions
    • C.T. Fulton, Two-point boundary value problems with eigenvalue parameter contained in the boundary conditions, Proc. R. Soc. Edinb. A 77 (1977), 293-308.
    • (1977) Proc. R. Soc. Edinb. A , vol.77 , pp. 293-308
    • Fulton, C.T.1
  • 15
    • 84971128441 scopus 로고
    • Singular eigenvalue problems with eigenvalue-parameter contained in the boundary conditions
    • C.T. Fulton, Singular eigenvalue problems with eigenvalue-parameter contained in the boundary conditions, Proc. R. Soc. Edinb. A87 (1980), 1-34.
    • (1980) Proc. R. Soc. Edinb. A , vol.87 , pp. 1-34
    • Fulton, C.T.1
  • 16
    • 0000055885 scopus 로고
    • Eigenfunction expansions for a singular eigenvalue problem with eigenparameter in the boundary conditions
    • D.B. Hinton, Eigenfunction expansions for a singular eigenvalue problem with eigenparameter in the boundary conditions, SIAM J. Math. Analysis 12 (1981), 572-584.
    • (1981) SIAM J. Math. Analysis , vol.12 , pp. 572-584
    • Hinton, D.B.1
  • 17
    • 0011227082 scopus 로고
    • Differential operators with spectral parameter incompletely in the boundary conditions
    • D.B. Minton and J.K. Shaw, Differential operators with spectral parameter incompletely in the boundary conditions, Funkcialaj Ekvacioj 33 (1990), 363-385.
    • (1990) Funkcialaj Ekvacioj , vol.33 , pp. 363-385
    • Minton, D.B.1    Shaw, J.K.2
  • 19
    • 0000224321 scopus 로고
    • On operators generated by elliptic boundary problems with a spectral parameter in boundary conditions
    • A. Kozhevnikov and S. Yakubov, On operators generated by elliptic boundary problems with a spectral parameter in boundary conditions, Integ. Eqns Operat. Theory 23 (1995), 205-231.
    • (1995) Integ. Eqns Operat. Theory , vol.23 , pp. 205-231
    • Kozhevnikov, A.1    Yakubov, S.2
  • 20
    • 0001116357 scopus 로고
    • Determination of a differential equation from two of its spectra
    • B.M. Levitan and M.G. Gasymov, Determination of a differential equation from two of its spectra, Russ. Math. Surv. 19 (1964), 1-63.
    • (1964) Russ. Math. Surv. , vol.19 , pp. 1-63
    • Levitan, B.M.1    Gasymov, M.G.2
  • 21
    • 0001365622 scopus 로고
    • Operator treatment of boundary problems with spectral parameters entering via polynomials in the boundary conditions
    • E.M. Russakovskii, Operator treatment of boundary problems with spectral parameters entering via polynomials in the boundary conditions, Funct. Analysis Applic. 9 (1975), 358-359.
    • (1975) Funct. Analysis Applic. , vol.9 , pp. 358-359
    • E.M. Russakovskii1
  • 22
    • 0000903601 scopus 로고    scopus 로고
    • The matrix Sturm-liouville problem with spectral parameter in the boundary conditions. Algebraic and operator aspects
    • E.M. Russakovskii, The matrix Sturm-Liouville problem with spectral parameter in the boundary conditions. Algebraic and operator aspects, Trans. Moscow Math. Soc. 57 (1996), 159-184.
    • (1996) Trans. Moscow Math. Soc. , vol.57 , pp. 159-184
    • E.M. Russakovskii1
  • 23
    • 0000653512 scopus 로고
    • Boundary problems for ordinary differential equations with parameter in the boundary conditions
    • A.A. Shkalikov, Boundary problems for ordinary differential equations with parameter in the boundary conditions, J. Soviet Math. 33 (1986), 1311-1342.
    • (1986) J. Soviet Math. , vol.33 , pp. 1311-1342
    • Shkalikov, A.A.1
  • 24
    • 0001045341 scopus 로고
    • On spectral functions of differential operators
    • A.V. Štraus, On spectral functions of differential operators, Izv. Akad. Nauk SSSR Ser. Mat. 19 (1955), 201-220.
    • (1955) Izv. Akad. Nauk SSSR Ser. Mat. , vol.19 , pp. 201-220
    • Štraus, A.V.1
  • 25
    • 0012317021 scopus 로고
    • On λ-nonlinear boundary eigenvalue problems
    • Akademie
    • C. Tretter, On λ-nonlinear boundary eigenvalue problems, Mathematics Research, vol. 71 (Akademie, 1993).
    • (1993) Mathematics Research , vol.71
    • Tretter, C.1
  • 26
    • 34250440396 scopus 로고
    • Regular eigenvalue problems with eigenparameter in the boundary conditions
    • J. Walter, Regular eigenvalue problems with eigenparameter in the boundary conditions, Math. Z. 133 (1973), 301-312.
    • (1973) Math. Z. , vol.133 , pp. 301-312
    • Walter, J.1
  • 27
    • 0011250131 scopus 로고
    • An expansion theorem for an eigenvalue problem on an arbitrary multiply connected domain with an eigenparameter in a general type of boundary conditions
    • E.M.E. Zayed and S.F.M. Ibrahim, An expansion theorem for an eigenvalue problem on an arbitrary multiply connected domain with an eigenparameter in a general type of boundary conditions, Acta Math. Sinica (NS) 11 (1995), 399-407.
    • (1995) Acta Math. Sinica (NS) , vol.11 , pp. 399-407
    • Zayed, E.M.E.1    Ibrahim, S.F.M.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.