Nonlinear Functional Boundary Value Problems in Banach Algebras Involving Carathéodories

  • Received : 2005.07.13
  • Published : 2006.12.23

Abstract

In this paper, an existence theorem for a nonlinear two point boundary value problem of second order differential equations in Banach algebras is proved using a nonlinear alternative based on Leray-Schauder alternative.

Keywords

References

  1. P. B. Bailey, L. F. Shampine and P. E. Waltman, Nonlinear Two Point Boundary Value Problems, Academic Press, New York, 1968.
  2. J. Banas, Fixed points of the product of the operators in Banach algebras, PanAmer. Math. J., 12(2)(2002), 101-109.
  3. J. Banas and K. Goebel, Measures of Noncompactness in Banach Spaces, LNPAM Vol. 60, Marcel Dekker, New York, 1980.
  4. S. R. Bernfield and V. Lakshmikantham, An Introduction to Nonlinear Boundary Value Problems, Academic Press, New York, 1980.
  5. K. Deimling, Nonlinear Functional Analysis, Springer Verlag, 1985.
  6. B. C. Dhage, A functional integro-differential equation in Banach algebras, Functional Differential Equations 11(3-4)(2004), 321-332.
  7. B. C. Dhage and S. K. Ntouyas, Existence theorems for nonlinear functional boundary value problems, Math. Sci. Res. J., 6(8)(2002), 380-390.
  8. B. C. Dhage, U. P. Dolhare and S. K. Ntouyas, Existence theorems for nonlinear first order functional differential equations in Banach algebras, Comm. Appl. Nonlinear Anal., 10(4)(2003), 59-69.
  9. B. C. Dhage and D. O'Regan, A fixed point theorem in Banach algebras with applications to functional integral equations, Functional Differential Equations, 7(3-4)(200), 257-267.
  10. A. Granas, R. B. Guenther and J. W. Lee, Some general existence principles in the Caratheodory theory of nonlinear differential systems, J. Math. Pures et Appl., 70(1991), 153-196.
  11. J. Henderson, Boundary Value Problems of Functional Differential Equations, World Scientific, Singapore, 1995.
  12. E. Zeidler, Nonlinear Functional Analysis and Its Applications : Part I, Springer Verlag, 1985.