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)



On Sturmian theory for second order systems

Author: Shair Ahmad
Journal: Proc. Amer. Math. Soc. 87 (1983), 661-665
MSC: Primary 34C10; Secondary 34A30
MathSciNet review: 687636
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: A generalization of the Sturm Comparison Theorem is given to nonselfadjoint second order linear systems. In addition, a theorem, involving the existence of a solution with strictly positive components, is proven. Counterexamples are given to show that the theorems are false without the stated assumptions.

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

  • [1] S. Ahmad and A. C. Lazer, On the components of extremal solutions of second order system, SIAM J. Math. Anal. 8 (1977), 16-23. MR 0430409 (55:3414)
  • [2] -, An $ N$-dimensional extension of the Sturm separation and comparison theory to a class of nonselfadjoint systems, SIAM J. Math. Anal. 9 (1978), 1137-1150. MR 512517 (80a:34035)
  • [3] -, Positive operators and Sturmian theory of nonselfadjoint second order systems. Nonlinear Equations in Abstract Spaces, Academic Press, New York, 1978. pp. 25-42. MR 502533 (80m:34027)
  • [4] -, A new generalizatin of the Sturm comparison theorem to selfadjoint systems, Proc. Amer. Math. Soc. 68 (1978), 185-188. MR 0470327 (57:10085)
  • [5] -, On an extension of Sturm's comparison theorem to a class of nonselfadjoint second order systems, Nonlinear Anal. 4 (1980), 497-501. MR 574368 (81g:34034)
  • [6] S. Ahmad, On positivity of solutions and conjugate points of nonselfadjoint systems, Bull. Acad. Polon. Sci. Math. Astronom. Phys. 27 (1979), 71-75. MR 539335 (80h:34038)
  • [7] S. Ahmad and J. A. Salazar, Conjugate points and second order systems, J. Math. Anal. Appl. 84 (1981), 63-72. MR 639525 (83a:34037)
  • [8] W. A. Coppel, Disconjugacy, Lecture Notes in Math., vol. 220, Springer-Verlag, Berlin and New York, 1971. MR 0460785 (57:778)
  • [9] M. Morse. A generalization of the Sturm separation and comparison theorems in $ n$-space, Math. Ann. 103 (1930), 72-90.
  • [10] K. Schmitt and H. L. Smith, Positive solutions and conjugate points for systems of differential equations, Nonlinear Anal. 2 (1978), 93-105. MR 512658 (80a:34033)
  • [11] J. C. F. Sturm, Mémoire sur les équations différentielles linéaires de second ordre, J. Math. Pures Appl. 1 (1836), 106-186.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 34C10, 34A30

Retrieve articles in all journals with MSC: 34C10, 34A30

Additional Information

Keywords: Conjugate point, disconjugate, irreducible, symmetric, selfadjoint, solution
Article copyright: © Copyright 1983 American Mathematical Society

American Mathematical Society