Triple Positive Solutions and Dependence on Higher Order Derivatives

Journal of Mathematical Analysis and Applications

Volumn 237, Issue 2, 1999, Pages 710-720

  Davis, John M ^a   Eloe, Paul W ^b   Henderson, Johnny ^a  

^a AUBURN UNIVERSITY   (United States)

^b UNIVERSITY OF DAYTON   (United States)

Author keywords

Fixed points; Green's function; Lidstone boundary value problem; Multiple solutions

Indexed keywords

EID: 0001109072     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmaa.1999.6500     Document Type: Article

References (20)

1. R. P. Agarwal and P. J. Y. Wong, Lidstone polynomials and boundary value problems, Comput. Math. Appl. 17 (1989), 1397-1421.
2. D. Anderson, Multiple positive solutions for a three-point boundary value problem, Math. Comput. Modelling, in press.
3. R. Avery, Existence of multiple positive solutions to a conjugate boundary value problem, MSR Hotline 2, No. 1 (1998).
4. E. Coddington and N. Levinson, "Theory of Ordinary Differential Equations," McGraw-Hill, New York, 1955.
5. J. M. Davis, Differentiability of solutions of differential equations with respect to nonlinear Lidstone boundary conditions, Nonlinear Differential Equations, in press.
6. J. M. Davis, Differentiation of solutions of Lidstone boundary value problems with respect to the boundary data, Math. Comput. Modelling, in press.
7. J. M. Davis, P. W. Eloe, and J. Henderson Comparison of eigenvalues for discrete Lidstone boundary value problems, Dynam. Systems Appl., in press.
8. J. M. Davis and J. Henderson, Triple positive symmetric solutions for a Lidstone boundary value problem, Differential Equations Dynam. Systems, in press.
9. J. M. Davis and J. Henderson, Uniqueness implies existence for fourth order Lidstone boundary value problems, Panamer. Math. J. 8 (1998), 23-35.
10. K. Deimling, "Nonlinear Functional Analysis," Springer-Verlag, New York, 1985.
11. P. W. Eloe, J. Henderson, and B. Thompson, Extremal points for impulsive Lidstone boundary value problems, Math. Comput. Modelling, in press.
12. D. Guo and V. Lakshmikantham, "Nonlinear Problems in Abstract Cones," Academic Press, San Diego, 1988.
13. J. Henderson and H. B. Thompson, Existence of multiple solutions for some nth order boundary value problems, preprint.
14. J. Henderson and H. B. Thompson, Multiple symmetric solutions for a second order boundary value problem, preprint.
15. T. M. Lamar, "Analysis of a 2nth Order Differential Equation with Lidstone Boundary Conditions," Ph.D. dissertation, Auburn University, 1997.
16. T. M. Lamar, Comparison theory for eigenvalue problems with Lidstone boundary conditions, preprint.
17. R. Leggett and L. Williams, Multiple positive fixed points of nonlinear operators on ordered Banach spaces, Indiana Univ. Math. J. 28 (1979), 673-688.
18. P. J. Y. Wong, Triple positive solutions of conjugate boundary value problems, Comput. Math. Appl. 36 (1998), 19-35.
19. P. J. Y. Wong and R. P. Agarwal, Multiple solutions of difference equations with Lidstone conditions, preprint.
20. P. J. Y. Wong and R. P. Agarwal, Results and estimates on multiple solutions of Lidstone boundary value problems, preprint.