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Volumn 130, Issue 10, 2002, Pages 3005-3015

Positive eigenvalues of second order boundary value problems and a theorem of M. G. Krein

Author keywords

Opial inequality; Positive eigenvalues; Stable boundedness

Indexed keywords


EID: 0036787012     PISSN: 00029939     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9939-02-06392-X     Document Type: Conference Paper
Times cited : (6)

References (21)
  • 3
    • 0002847423 scopus 로고
    • Eigenvalue ratios for Sturm-Liouville operators
    • MR 94c:34125
    • M. S. Ashbaugh and R. D. Benguria, Eigenvalue ratios for Sturm-Liouville operators, J. Diff. Eqs. 103 (1993), 205-219. MR 94c:34125
    • (1993) J. Diff. Eqs. , vol.103 , pp. 205-219
    • Ashbaugh, M.S.1    Benguria, R.D.2
  • 4
    • 0040768160 scopus 로고
    • Extremal problems for eigenvalues of the Sturm-Liouville type
    • Birkhäuser, Basel, MR 90k:34020
    • C. Bandle, Extremal problems for eigenvalues of the Sturm-Liouville type, In General In-equalities, 5, Birkhäuser, Basel, 1987, 319-339. MR 90k:34020
    • (1987) General In-equalities , vol.5 , pp. 319-339
    • Bandle, C.1
  • 5
    • 33749236104 scopus 로고
    • Optimal bounds for the spectrum of a one-dimensional operator
    • Birkhäuser, Basel, MR 94c:34126
    • C. Bennewitz and E. J. M. Veling, Optimal bounds for the spectrum of a one-dimensional operator, In General Inequalities, 6, Birkhäuser, Basel, 1992, 257-268. MR 94c:34126
    • (1992) General Inequalities , vol.6 , pp. 257-268
    • Bennewitz, C.1    Veling, E.J.M.2
  • 6
    • 0010564661 scopus 로고    scopus 로고
    • Applications of a one-dimensional Sobolev inequality to eigenvalue problems
    • MR 96k:34180
    • R. C. Brown, D. B. Hinton and S. Schwabik, Applications of a one-dimensional Sobolev inequality to eigenvalue problems, Diff. and Integral Eqs. 9 (1996), 481-498. MR 96k:34180
    • (1996) Diff. and Integral Eqs. , vol.9 , pp. 481-498
    • Brown, R.C.1    Hinton, D.B.2    Schwabik, S.3
  • 7
    • 0010530634 scopus 로고    scopus 로고
    • private communication, September
    • R. C. Brown, private communication, September, 2000.
    • (2000)
    • Brown, R.C.1
  • 8
    • 0002939803 scopus 로고    scopus 로고
    • Some opial, lyapunov, and de la valée poussin inequalities with nonhomogeneous boundary conditions
    • MR 2000m:34073
    • R. C. Brown, A. M. Fink, and D. B. Hinton, Some Opial, Lyapunov, and De la Valée Poussin inequalities with nonhomogeneous boundary conditions, J. of Inequal. and Appl. 5 (2000), 11-37. MR 2000m:34073
    • (2000) J. of Inequal. and Appl. , vol.5 , pp. 11-37
    • Brown, R.C.1    Fink, A.M.2    Hinton, D.B.3
  • 9
    • 0000713287 scopus 로고    scopus 로고
    • A Liapunov inequality for linear Hamiltonian systems
    • MR 99c:34056
    • S. Clark and D. Hinton, A Liapunov inequality for linear Hamiltonian systems, Math. Inequalities and Appl. 1 (1998), 201-209. MR 99c:34056
    • (1998) Math. Inequalities and Appl. , vol.1 , pp. 201-209
    • Clark, S.1    Hinton, D.2
  • 10
    • 0003249268 scopus 로고
    • Disconjugacy
    • Springer-Verlag, Berlin, MR 57:778
    • W. A. Coppel, Disconjugacy, Lecture Notes in Mathematics 220, Springer-Verlag, Berlin, 1971. MR 57:778
    • (1971) Lecture Notes in Mathematics , vol.220
    • Coppel, W.A.1
  • 11
    • 0034373412 scopus 로고    scopus 로고
    • A hierarchical method for obtaining eigenvalue enclosures
    • MR 2001a:34148
    • E. B. Davies, A hierarchical method for obtaining eigenvalue enclosures, Math. of Computation, 69 (2000), 1435-1455. MR 2001a:34148
    • (2000) Math. of Computation , vol.69 , pp. 1435-1455
    • Davies, E.B.1
  • 13
    • 21144463535 scopus 로고
    • The ground state energy of schrödinger operators
    • MR 93j:47070
    • F. Gesztesy, G. M. Graf and B. Simon, The ground state energy of Schrödinger operators, Commun. Math. Phys. 150 (1992), 375-384. MR 93j:47070
    • (1992) Commun. Math. Phys. , vol.150 , pp. 375-384
    • Gesztesy, F.1    Graf, G.M.2    Simon, B.3
  • 15
    • 0002714045 scopus 로고
    • On tests for stable boundedness of solutions of periodic canonical systems
    • M. G. Krein, On tests for stable boundedness of solutions of periodic canonical systems, Amer. Math. Soc. Transl. Ser. (2), 120 (1983), 71-110.
    • (1983) Amer. Math. Soc. Transl. Ser. (2) , vol.120 , pp. 71-110
    • Krein, M.G.1
  • 16
    • 0001146164 scopus 로고
    • On certain problems of the maximum and minimum of characteristic values and on the Lyapunov zones of stability
    • MR 17:484e
    • M. G. Krein, On certain problems of the maximum and minimum of characteristic values and on the Lyapunov zones of stability, Amer. Math. Soc. Transl. Ser. (2), 1 (1955), 163-187. MR 17:484e
    • (1955) Amer. Math. Soc. Transl. Ser. (2) , vol.1 , pp. 163-187
    • Krein, M.G.1
  • 18
    • 0000648581 scopus 로고
    • Eigenvalue inclusions for second order ordinary differential operators by a numerical homotopy method
    • MR 91d:65116
    • M. Plum, Eigenvalue inclusions for second order ordinary differential operators by a numerical homotopy method, Z. Angew. Math. Phys. 41 (1990), 205-226. MR 91d:65116
    • (1990) Z. Angew. Math. Phys. , vol.41 , pp. 205-226
    • Plum, M.1


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