A generalization of concavity for finite differences

Computers and Mathematics with Applications

Volumn 36, Issue 10-12, 1998, Pages 109-113

  Eloe, P W ^a  

^a UNIVERSITY OF DAYTON   (United States)

Author keywords

Concavity; Finite differences; Green's function

Indexed keywords

BOUNDARY CONDITIONS; GREEN'S FUNCTION; POLYNOMIALS;

PIECEWISE POLYNOMIALS;

FINITE DIFFERENCE METHOD;

EID: 0032205820     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0898-1221(98)80013-8     Document Type: Article

References (17)

1. J.A. Gaticia, V. Oliker and P. Waltman, Iterative procedures for nonlinear second order boundary value problems, Ann. Mat. Pur. Appl. 157, 1-25 (1989).
2. J.A. Gatica, V. Oliker and P. Waltman, Singular nonlinear boundary value problems for second-order differential equations, J. Differential Equations 79, 62-78 (1989).
3. P.W. Eloe and J. Henderson, Singular nonlinear boundary value problems for higher order ordinary differential equations, Nonlin. Anal. 17, 1-10 (1991).
4. L.H. Erbe and H. Wang, On the existence of positive solutions of ordinary differential equations, Proc. Amer. Math. Soc. 120, 743-748 (1994).
5. L.H. Erbe and H. Wang, Existence and nonexistence of positive solutions in annular regions, WSSIAA 3, 207-217 (1994).
6. H. Wang, On the existence of positive solutions for semilinear elliptic equations in the annulus, J. Differential Equations 109, 1-7 (1994).
7. M.A. Krasnosel'skii, Positive Solutions of Operator Equations, Noordhoff, Gronongen, (1964).
8. P.W. Eloe and J. Henderson, Positive solutions for higher order ordinary differential equations, Electronic J. of Differential Equations 3, 1-8 (1995).
9. P.W. Eloe, J. Henderson and P.J.Y. Wong, Positive solutions for two-point boundary value problems, In Dyn. Sys. & Appl., Volume 2, pp. 135-144, Dynamic Publishers, Atlanta, GA, (1996).
10. J. Henderson and H. Wang, Positive solutions for nonlinear eigenvalue problems (preprint).
11. R.P. Agarwal and P.J.Y. Wong, On the existence of solutions of singular boundary value problems for higher order difference equations, Nonlin. Anal. (to appear).
12. J. Henderson and E. Kaufmann, On the existence of solutions of focal boundary value problems for singular difference equations, Computers Math. Applic. (to appear).
13. F. Merdivenci, Green's matrices and positive solutions of a discrete boundary value problem, PanAmer. Math. Journal 5, 25-42 (1995).
14. P.W. Eloe and J. Henderson, Inequalities based on a generalization of concavity, Proc. Amer. Math. Soc. 125, 2103-2108 (1997).
15. P.W. Eloe and J. Henderson, Singular nonlinear (n - 1, 1) conjugate boundary value problems, Georgian Math Journal 4, 501-512 (1997).
16. P.W. Eloe and J. Henderson, Positive solutions for (n - 1, 1) conjugate boundary value problems, Nonlin. Anal. 28, 1669-1680 (1997).
17. P. Hartman, Difference equations: Disconjugacy, principal solutions, Green's functions, complete monotonicity, Trans. Amer. Math. Soc. 246, 1-30 (1978).