On an eigenvalue problem of Ahmad and Lazer for ordinary differential equations
Author:
Marcellino Gaudenzi
Journal:
Proc. Amer. Math. Soc. 99 (1987), 237-243
MSC:
Primary 34B25
DOI:
https://doi.org/10.1090/S0002-9939-1987-0870778-5
MathSciNet review:
870778
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: In connection with a problem posed by S. Ahmad and A. C. Lazer, we show the existence of a class of nonselfadjoint eigenvalue problems related to the equation for which the general eigenvalues comparison is not true. We use a comparison principle for the zeros of the corresponding Cauchy problem.
- [1] Shair Ahmad and Alan C. Lazer, On 𝑛th-order Sturmian theory, J. Differential Equations 35 (1980), no. 1, 87–112. MR 556794, https://doi.org/10.1016/0022-0396(80)90051-0
- [2] Shair Ahmad and Alan C. Lazer, On an extension of the Sturm comparison theorem, SIAM J. Math. Anal. 12 (1981), no. 1, 1–9. MR 603413, https://doi.org/10.1137/0512001
- [3] G. J. Butler and L. H. Erbe, Integral comparison theorems and extremal points for linear differential equations, J. Differential Equations 47 (1983), no. 2, 214–226. MR 688103, https://doi.org/10.1016/0022-0396(83)90034-7
- [4] W. A. Coppel, Disconjugacy, Lecture Notes in Mathematics, Vol. 220, Springer-Verlag, Berlin-New York, 1971. MR 0460785
- [5] Uri Elias, Eigenvalue problems for the equations 𝐿𝑦+𝜆𝑝(𝑥)𝑦=0, J. Differential Equations 29 (1978), no. 1, 28–57. MR 0486759, https://doi.org/10.1016/0022-0396(78)90039-6
- [6] Uri Elias, Oscillatory solutions and extremal points for a linear differential equation, Arch. Rational Mech. Anal. 71 (1979), no. 2, 177–198. MR 525223, https://doi.org/10.1007/BF00248726
- [7]
-, The extremal solutions of the equations
. II, J. Math. Anal. Appl. 55 (1976), 253-265.
Retrieve articles in Proceedings of the American Mathematical Society with MSC: 34B25
Retrieve articles in all journals with MSC: 34B25
Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1987-0870778-5
Keywords:
Linear,
eigenvalue,
comparison,
extremal points
Article copyright:
© Copyright 1987
American Mathematical Society