Focal points for a linear differential equation whose coefficients are of constant signs

Author:
Uri Elias

Journal:
Trans. Amer. Math. Soc. **249** (1979), 187-202

MSC:
Primary 34C10; Secondary 34A30, 34B05

DOI:
https://doi.org/10.1090/S0002-9947-1979-0526317-1

MathSciNet review:
526317

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Abstract: The differential equation considered is , where . The focal point is defined as the least value of s, , such that there exists a nontrivial solution *y* which satisfies and , . Our method is based on a characterization of by solutions which satisfy , on , . We study the behavior of the function and the dependence of on when at least a certain does not vanish identically near *a* or near . As an application we prove the existence of an eigenvalue of a related boundary value problem.

**[1]**G. A. Bogar,*Properties of two point boundary value functions*, Proc. Amer. Math. Soc.**23**(1969), 335-339. MR**0247166 (40:435)****[2]**W. A. Coppel,*Stability and asymptotic behaviour of differential equations*, Heath, Boston, Mass., 1965. MR**0190463 (32:7875)****[3]**R. D. Gentry and C. C. Travis,*Comparison of eigenvalues associated with linear differential equations of arbitrary order*, Trans. Amer. Math. Soc.**223**(1976), 167-179. MR**0425241 (54:13198)****[4]**P. Hartman,*Ordinary differential equations*, Wiley, New York, London, Sidney, 1964. MR**0171038 (30:1270)****[5]**M. S. Keener and C. C. Travis,*Positive cones and focal points for a class of nth order differential equations*, Trans. Amer. Math. Soc.**237**(1978), 331-351. MR**479377 (80i:34050)****[6]**Z. Nehari,*Green's functions and disconjugacy*, Arch. Rational Mech. Anal.**62**(1976), 53-76. MR**0412519 (54:642)****[7]**C. C. Travis,*Comparison of eigenvalues for linear differential equations of order*2*n*, Trans. Amer. Math. Soc.**177**(1973), 363-374. MR**0316808 (47:5356)**

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DOI:
https://doi.org/10.1090/S0002-9947-1979-0526317-1

Article copyright:
© Copyright 1979
American Mathematical Society