Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Sign properties of Green's functions for a family of two-point boundary value problems


Authors: Paul W. Eloe and Jerry Ridenhour
Journal: Proc. Amer. Math. Soc. 120 (1994), 443-452
MSC: Primary 34C10; Secondary 34B27
DOI: https://doi.org/10.1090/S0002-9939-1994-1172948-1
MathSciNet review: 1172948
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Sign properties of and comparison theorems for Green's functions of a family of two-point boundary value problems for a general ordinary differential operator are obtained. The results extend known results for a two-term ordinary differential operator.


References [Enhancements On Off] (What's this?)

  • [1] P. W. Bates and G. B. Gustafson, Maximization of Green's functions over classes of multipoint boundary value problems, SIAM J. Math. Anal. 7 (1976), 858-871. MR 0450653 (56:8946)
  • [2] E. A. Coddington and N. Levinson, Theory of ordinary differential equations, McGraw-Hill, New York (1955). MR 0069338 (16:1022b)
  • [3] W. Coppel, Disconjugacy, Lecture Notes in Math., vol. 220, Springer-Verlag, New York and Berlin, 1971. MR 0460785 (57:778)
  • [4] U. Elias, Green's functions for a nondisconjugate differential operator, J. Differential Equations 37 (1980), 318-350. MR 589996 (82h:34028)
  • [5] P. W. Eloe, Sign properties of Green's functions for two classes of boundary value problems, Canad. Math. Bull. 30 (1987), 28-35. MR 879867 (88f:34036)
  • [6] P. W. Eloe, D. Hankerson, and J. Henderson, Positive solutions and conjugate points for multipoint boundary value problems, J. Differential Equations 95 (1992), 20-32. MR 1142275 (92j:34033)
  • [7] -, Positive solutions and $ j$-focal points for two point boundary value problems, Rocky Mountain J. Math. 22 (1992), 1283-1293. MR 1201092 (94f:34047)
  • [8] P. W. Eloe and J. Henderson, Focal points and comparison theorems for a class of two point boundary value problems, J. Differential Equations 102 (1993). MR 1221911 (94i:34041)
  • [9] G. B. Gustafson, A Green's function convergence principle, with applications to computation and norm estimates, Rocky Mountain J. Math. 6 (1976), 457-492. MR 0414978 (54:3070)
  • [10] A. Ju. Levin, Non-oscillation of solutions of the equation $ {x^{(n)}} + {p_1}(t){x^{(n - 1)}} + \cdots + {p_n}(t)x = 0$, Russian Math. Surveys 24 (1969), 43-99. MR 0254328 (40:7537)
  • [11] J. S. Muldowney, A necessary and sufficient condition for disfocality, Proc. Amer. Math. Soc. 74 (1979), 49-55. MR 521872 (80c:34030)
  • [12] -, On invertibility of linear ordinary differential boundary value problems, SIAM J. Math. Anal. 12 (1981), 368-384. MR 613318 (82g:34018)
  • [13] Z. Nehari, Disconjugate linear differential operators, Trans. Amer. Math. Soc. 129 (1967), 500-516. MR 0219781 (36:2860)
  • [14] -, Green's functions and disconjugacy, Arch. Rational Mech. Anal. 62 (1976), 53-76. MR 0412519 (54:642)
  • [15] A. Peterson, On the sign of the Green's function beyond the interval of disconjugacy, Rocky Mountain J. Math. 3 (1973), 41-51. MR 0326069 (48:4414)
  • [16] -, On the sign of the Green's functions, J. Differential Equations 21 (1976), 167-178.
  • [17] -, Green's functions for focal type boundary value problems, Rocky Mountain J. Math. 9 (1979), 721-732. MR 560249 (81i:34022)
  • [18] -, Focal Green's functions for fourth-order differential equations, J. Math. Anal. Appl. 75 (1980), 602-160. MR 581843 (81i:34023)
  • [19] A. Peterson and J. Ridenhour, Comparison theorems for Green's functions for focal boundary value problems, Recent Trends in Ordinary Differential Equations, World Sci. Ser. Appl. Anal., vol. 1, World Sci. Publ., Teaneck, NJ, 1992, pp. 493-506. MR 1180134 (94b:34048)
  • [20] E. L. Reiss, A. J. Callegari, and D. S. Ahluwalia, Ordinary differential equations with applications, Holt, Rinehart, and Winston, New York, 1976.
  • [21] J. Ridenhour, On the sign of Green's functions for multipoint boundary value problems, Pacific J. Math. 92 (1981), 141-150. MR 618052 (82k:34027)
  • [22] -, Green's functions and linear boundary value problems, J. Differential Equations 39 (1981), 259-268. MR 607785 (82k:34026)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 34C10, 34B27

Retrieve articles in all journals with MSC: 34C10, 34B27


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1994-1172948-1
Article copyright: © Copyright 1994 American Mathematical Society

American Mathematical Society