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)

 
 

 

Boundary value problems for second order nonlinear matrix differential equations


Author: Warren E. Shreve
Journal: Proc. Amer. Math. Soc. 83 (1981), 63-68
MSC: Primary 34B15
DOI: https://doi.org/10.1090/S0002-9939-1981-0619982-6
MathSciNet review: 619982
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Existence of a solution to $ X'' = F(t,X,X')$, $ X(a) = A$, $ X(b) = B$, is shown under certain conditions using a degree-theoretic result similar to one of Bebernes where $ X,F,A,B$ are $ n \times n$ matrices.


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

  • [1] J. W. Bebernes, A simple alternative problem for finding periodic solutions of second order ordinary differential systems, Proc. Amer. Math. Soc. 42 (1974), 121-127. MR 0330597 (48:8934)
  • [2] J. W. Bebernes and K. Schmitt, Periodic boundary value problems for systems of second order differential equations, J. Differential Equations 13 (1973), 32-47. MR 0340700 (49:5451)
  • [3] R. Bellman, Introduction to matrix analysis, McGraw-Hill, New York, 1970. MR 0258847 (41:3493)
  • [4] L. Fountain and L. Jackson, A generalized solution of the boundary value problem for $ y'' = f(x,y,y') $, Pacific J. Math. 12 (1962), 1251-1272. MR 0163002 (29:305)
  • [5] P. Hartman, Ordinary differential equations, Wiley, New York, 1964. MR 0171038 (30:1270)
  • [6] K. A. Heimes, Two point boundary problems in Banach space, J. Differential Equations 5 (1969), 215-225. MR 0240430 (39:1779)
  • [7] -, Green's functions for linear second order systems, SIAM J. Math. Anal. 9 (1978), 207-214. MR 0463602 (57:3547)
  • [8] L. K. Jackson, Subfunctions and second-order ordinary differential inequalities, Adv. in Math. 2 (1968), 307-363. MR 0229896 (37:5462)
  • [9] K. Schmitt, Periodic solutions of systems of second-order differential equations, J. Differential Equations 11 (1972), 180-192. MR 0294790 (45:3858)
  • [10] J. Schwartz, Nonlinear functional analysis, McGraw-Hill, New York, 1970.
  • [11] E. C. Tomastik, Oscillation of nonlinear matrix differential equations of the second order, Proc. Amer. Math. Soc. 19 (1968), 1427-1431. MR 0232046 (38:372)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 34B15

Retrieve articles in all journals with MSC: 34B15


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1981-0619982-6
Keywords: Nonlinear matrix differential equations, boundary value problems, degree theory
Article copyright: © Copyright 1981 American Mathematical Society

American Mathematical Society