Positive Solutions of Difference Equations with Two-Point Right Focal Boundary Conditions

Journal of Mathematical Analysis and Applications

Volumn 224, Issue 1, 1998, Pages 34-58

  Wong, Patricia J Y ^a  

^a NANYANG TECHNOLOGICAL UNIVERSITY   (Singapore)

Author keywords

Positive solutions; difference equatons; boundary value problems

Indexed keywords

EID: 0002814781     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmaa.1998.5983     Document Type: Article

References (44)

1. Agarwal R. P. Boundary Value Problems for Higher Order Differential Equations. 1986;World Scientific, Singapore.
2. Agarwal R. P. Difference Equations and Inequalities. 1992;Dekker, New York.
3. Agarwal R. P., Henderson J., Wong P. J. Y. On superlinear and sublinear (np. Nonlinear World. 4:1997;101-115.
4. Agarwal R. P., Wong P. J. Y. Existence of solutions for singular boundary value problems for higher order differential equations. Rend. Sem. Math. Fis. Milano. 55:1995;249-264.
5. Agarwal R. P., Wong P. J. Y. Advanced Topics in Difference Equations. 1997;Kluwer Academic, Dordrecht.
6. Aronson D., Crandall M. G., Peletier L. A. Stabilization of solutions of a degenerate nonlinear diffusion problem. Nonlinear Anal. 6:1982;1001-1022.
7. F. Atici, A. C. Peterson, Bound for positive solutions for a focal boundary value problem, in, Advances in Difference Equations II, Comput. Math. Appl.
8. Bandle C., Coffman C. V., Marcus M. Nonlinear elliptic problems in annular domains. J. Differential Equations. 69:1987;322-345.
9. Bandle C., Kwong M. K. Semilinear elliptic problems in annular domains. J. Appl. Math. Phys. 40:1989;245-257.
10. Choi Y. S., Ludford G. S. An unexpected stability result of the near-extinction diffusion flame for non-unity Lewis numbers. Quart. J. Mech. Appl. Math. 42:1989;143-158.
11. Chyan C. J., Henderson J. Positive solutions for singular higher order nonlinear equations. Differential Equations Dynam. Systems. 2:1994;153-160.
12. Cohen D. S. Multiple stable solutions of nonlinear boundary value problems arising in chemical reactor theory. SIAM J. Appl. Math. 20:1971;1-13.
13. Dancer E. N. On the structure of solutions of an equation in catalysis theory when a parameter is large. J. Differential Equations. 37:1980;404-437.
14. Eloe P. W., Henderson J. Positive solutions for higher order ordinary differential equations. Electron. J. Differential Equations. 3:1995;1-8.
15. Eloe P. W., Henderson J. Positive solutions for (n. Nonlinear Anal. 28:1997;1669-1680.
16. Erbe L. H., Hu S., Wang H. Multiple positive solutions of some boundary value problems. J. Math. Anal. Appl. 184:1994;640-648.
17. Erbe L. H., Wang H. On the existence of positive solutions of ordinary differential equations. Proc. Amer. Math. Soc. 120:1994;743-748.
18. Fink A. M. The radial Laplacian Gel'fand problem. Delay and Differential Equations. 1992;World Scientific, River Edge. p. 93-98.
19. Fink A. M., Gatica J. A., Hernandez G. E. Eigenvalues of generalized Gel'fand models. Nonlinear Anal. 20:1993;1453-1468.
20. u. Bull. Amer. Math. Soc. 75:1969;132-135.
21. Garaizar X. Existence of positive radial solutions for semilinear elliptic problems in the annulus. J. Differential Equations. 70:1987;69-72.
22. Gatica J. A., Oliker V., Waltman P. Singular nonlinear boundary value problems for second-order ordinary differential equations. J. Differential Equations. 79:1989;62-78.
23. Gel'fand I. M. Some problems in the theory of quasilinear equations. Uspekhi Mat. Nauk. 14:1959;87-158.
24. Guo D., Lakshmikantham V. Nonlinear Problems in Abstract Cones. 1988;Academic Press, San Diego.
25. Hankerson D., Peterson A. C. Comparison of eigenvalues for focal point problems forn. Differential Integral Equations. 3:1990;363-380.
26. Henderson J. Singular boundary value problems for difference equations. Dynam. Systems Appl. 1:1992;271-282.
27. Henderson J. Singular boundary value problems for higher order difference equations. Lakshmikantham V. Proceedings of the First World Congress on Nonlinear Analysts. 1996;1139-1150 de Gruyter, Berlin.
28. Krasnosel'skii M. A. Positive Solutions of Operator Equations. 1964;Noordhoff, Groningen.
29. Merdivenci F. Two positive solutions of a boundary value problem for difference equations. J. Diff. Equations Appl. 1:1995;262-270.
30. Merdivenci F. Green's matrices and positive solutions of a discrete boundary value problem. Panamer. Math. J. 5:1995;25-42.
31. Merdivenci F. Positive solutions for focal point problems for 2n. Panamer. Math. J. 5:1995;71-82.
32. O'Regan D. Theory of Singular Boundary Value Problems. 1994;World Scientific, Singapore.
33. Parter S. Solutions of differential equations arising in chemical reactor processes. SIAM J. Appl. Math. 26:1974;687-716.
34. Peterson A. C. Boundary value problems for ann. SIAM J. Math. Anal. 15:1984;124-132.
35. Wang H. On the existence of positive solutions for semilinear elliptic equations in the annulus. J. Differential Equations. 109:1994;1-7.
36. P. J. Y. Wong, Two-point right focal eigenvalue problems for difference equations, Dynam. Systems Appl.
37. Wong P. J. Y., Agarwal R. P. Eigenvalues of boundary value problems for higher order differential equations. Math. Problems Engrg. 2:1996;401-434.
38. Wong P. J. Y., Agarwal R. P. Double positive solutions of (np. Comput. Math. Appl. 32:1996;1-21.
39. Wong P. J. Y., Agarwal R. P. On the existence of solutions of singular boundary value problems for higher order difference equations. Nonlinear Anal. 28:1997;277-287.
40. P. J. Y. Wong, R. P. Agarwal, On the existence of positive solutions of higher order difference equations, Topol. Methods Nonlinear Anal.
41. P. J. Y. Wong, R. P. Agarwal, On the eigenvalues of boundary value problems for higher order difference equations, Rocky Mountain J. Math.
42. Wong P. J. Y., Agarwal R. P. Eigenvalue characterization for (np. J. Austral. Math. Soc. Ser. B. 39:1998;386-407.
43. P. J. Y. Wong, R. P. Agarwal, Eigenvalues of annnp, Dynam. Continuous Discrete Impulsive Systems.
44. Wong P. J. Y., Agarwal R. P. On eigenvalue intervals and twin eigenfunctions of higher order boundary value problems. J. Comput. Appl. Math. 88:1998;15-43.