A comparison theorem for conjugate points of general selfadjoint differential equations
Author:
Kurt Kreith
Journal:
Proc. Amer. Math. Soc. 25 (1970), 656-661
MSC:
Primary 34.42
DOI:
https://doi.org/10.1090/S0002-9939-1970-0259246-9
MathSciNet review:
0259246
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Abstract: Comparison theorems for conjugate points of fourth order selfadjoint differential equations have been established by J. Barrett. In the present paper a more direct method of proof is used to generalize Barrett’s theorem to general selfadjoint equations of even order while replacing certain pointwise conditions on the coefficients by weaker integral conditions. Further generalizations are indicated to nonlinear equations, to differential inequalities, and to certain nonselfadjoint equations.
- John H. Barrett, Fourth order boundary value problems and comparison theorems, Canadian J. Math. 13 (1961), 625–638. MR 133519, DOI https://doi.org/10.4153/CJM-1961-051-x
- Robert W. Hunt, The behavior of solutions of ordinary, self-adjoint differential equations of arbitrary even order, Pacific J. Math. 12 (1962), 945–961. MR 147725
- H. C. Howard, Some oscillation criteria for general self-adjoint differential equations, J. London Math. Soc. 43 (1968), 401–406. MR 227520, DOI https://doi.org/10.1112/jlms/s1-43.1.401
- Robert L. Sternberg, Variational methods and non-oscillation theorems for systems of differential equations, Duke Math. J. 19 (1952), 311–322. MR 48668
- Kurt Kreith, A Picone identity for first order differential systems, J. Math. Anal. Appl. 31 (1970), 297–308. MR 261088, DOI https://doi.org/10.1016/0022-247X%2870%2990024-7
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Keywords:
Conjugate points,
matrix system,
fundamental system of solutions
Article copyright:
© Copyright 1970
American Mathematical Society