On the eigenvalue accumulation of Sturm-Liouville problems depending nonlinearly on the spectral parameter

Mathematische Nachrichten

Volumn 189, Issue , 1998, Pages 157-170

  Mennicken, R ^a   Schmid, H ^a   Shkalikov, A A ^b  

^a UNIVERSITY OF REGENSBURG   (Germany)

^b MOSCOW STATE UNIVERSITY   (Russian Federation)

Author keywords

Majorant pair; Nonoscillatory; Oscillatory; Suydams criterion

Indexed keywords

EID: 0000138487     PISSN: 0025584X     EISSN: None     Source Type: Journal    
DOI: 10.1002/mana.19981890110     Document Type: Article

References (19)

1. ADAM, J. A.: Critical Layer Singularities and Complex Eigenvalues in Some Differential Equations of Mathematical Physics, Phys. Rep. (Review Section of Physics Letters) 142, No. 5 (1986), 263-356
2. ASLANJAN, A., and LIDSKII, V.: Asymptotic Formula for Frequences of Lower Seria in Theory of Shells, Izvestija Acad. Sc. Armenian SSR, Ser. Matem. VI, No. 2-3 (1971), 113-130 (Russian)
3. GREENBERG, L., and BABUŠKA, I.: A Continuous Analogue of Sturm Sequences in the Context of Sturm-Liouville Equations, SIAM J. Numer. Anal. 26, No. 4 (1989), 920-945
4. GLAZMAN, I. M.: Direct Methods of the Qualitative Spectral Analysis of Singular Differential Operators, Fizmatgiz, Moscow, 1963 (Russian)
5. GOEDBLOED, J. P.: Lecture Notes on Ideal Magnetohydrodynamics, Rijnhuizen Report, Fom-Instituut voor Plasmafysica, Nieuwegein, 83-145, 1983
6. GRAD, H.: Magnetofluid-Dynamic Spectrum and Low Shear Stability, Proc. Nat. Acad. Sci. U. S. A. 70 (1973), 3277-3281
7. HARTMAN, P.: Ordinary Differential Equations, Birkhäuser-Verlag, Boston-Basel-Stuttgart, 1982
8. HARTMAN, P.: Boundary Value Problems of Second Order Ordinary Differential Equations Involving a Parameter, J. Diff. Equations 12 (1972), 194-212
9. HAIN, K., and LÜST, R.: Zur Stabilität zylindersymmetrischer Plasmakonfigurationen mit Volumenströmen, Z. Naturforsch. 13a (1958), 936-940
10. INCE, E. L.: Ordinary Differential Equations, Dover, 1956
11. KOKHOLM, N. J.: Spectral Analysis of Perturbed Multiplication Operators Occuring in Polymerization Chemistry, Proc. Royal Soc. Edingburgh 113a (1989), 119-148
12. KRYLOV, A. L., LIFSHITZ, A. E. and FYODOROV, E. N.: On the Resonant Properties of the Magnetosphere, Fizika Zemli 6 (1981), 49-58 (Russian)
13. LIFSHITZ, A. E.: Magnetohydrodynamics and Spectral Theory, Kluwer Acad. Publishers, Dodrecht, 1989
14. LANGER, H., MENNICKEN, M., and MÖLLER, M.: A Second Order Differential Operator Depending Nonlinearly on the Eigenvalue Parameter, in: Operator Theory: Advances and Applications, Vol. 48, Birkhäuser-Verlag, Basel, 319-332, 1990
15. MENNICKEN, R., SCHMID, H., and SHKALIKOV, A. A.: Criterion on the Eigenvalue Accumulation of Nonlinear Spectral Problems for Ordinary Differential Operators with Singularities, in: U. Helmke, R. Mennicken, J. Saurer (Eds.), Systems and Networks: Mathematical Theory and Applications, Vol. II, Akademie-Verlag, Berlin, 793-798, 1990
16. NAIMARK, M. A.: Linear Differential Operators, Frederick Ungar Publishing, New York, 1967
17. RAIKOV, G. D.: The Spectrum of a Linear Magnetodynamic Model with Cylindrical Symmetry, Arch. Rational Mech. Anal. 116 (1991), 161-198
18. REID, W. T.: Ordinary Differential Equations, John Wiley & Sons, New York, 1971
19. REID, W. T.: Boundary Problems of Sturmian Type on an Infinite Interval, SIAM J. Math. Anal. 4 (1973), 185-197