Positive solutions of discrete (n, p) boundary value problems

Nonlinear Analysis, Theory, Methods and Applications

Volumn 30, Issue 1, 1997, Pages 377-388

  Wong, Patricia J Y ^a  

^a NANYANG TECHNOLOGICAL UNIVERSITY   (Singapore)

Author keywords

Boundary value problems; Eigenvalues; Positive solutions

Indexed keywords

EID: 0042046400     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0362-546X(96)00139-3     Document Type: Article

References (37)

1. AGARWAL R. P., Difference Equations and Inequalities, Marcel Dekker, New York(1992).
2. AGARWAL R. P. & LALLI B. S., Discrete polynomial interpolation, Green's functions, maximum principles, error bounds and boundary value problems, Computers Math. Applic. 25, 3-39(1993).
3. AGARWAL R. P. & HENDERSON J., Superlinear and sublinear focal boundary value problems, Applicable Analysis 60, 189-200(1996).
4. AGARWAL R. P. & HENDERSON J., Positive solutions and nonlinear problems for third order difference equations, in Advances in Difference Equations II, Computers Math. Appl., to appear.
5. AGARWAL R. P., HENDERSON J. & WONG P. J. Y., On superlinear and sublinear (n, p) boundary value problems for higher order difference equations, Nonlinear World, to appear.
6. AGARWAL R. P. & WONG P. J. Y., Existence of solutions for singular boundary value problems for higher order differential equations, Rendiconti del Seminario Mathematico e Fisico di Milano, to appear.
7. ARONSON D., CRANDALL M. G. & PELETIER L. A., Stabilization of solutions of a degenerate nonlinear diffusion problem, Nonlinear Analysis 6, 1001-1022(1982).
8. BANDLE C., COFFMAN C. V. & MARCUS M., Nonlinear elliptic problems in annular domains, J. Diff. Eqns. 69, 322-345(1987).
9. BANDLE C. & KWONG M. K., Semilinear elliptic problems in annular domains, J. Appl. Math. Phys. 40, 245-257(1989).
10. CHOI Y. S. & LUDFORD G. S., An unexpected stability result of the near-extinction diffusion flame for non-unity Lewis numbers, Q. J. Mech. Appl. Math. 42, part 1, 143-158(1989).
11. CHYAN C. J. and HENDERSON J., Positive solutions for singular higher order nonlinear equations, Dig. Eqs. Dyn. Sys. 2, 153-160(1994).
12. COHEN D. S., Multiple stable solutions of nonlinear boundary value problems arising in chemical reactor theory, SIAM J. Appl. Math. 20, 1-13(1971).
13. DANCER E. N., On the structure of solutions of an equation in catalysis theory when a parameter is large, J. Diff. Eqns. 37, 404-437(1980).
14. ELOE P. W. & HENDERSON J., Singular nonlinear boundary value problems for higher order ordinary differential equations, Nonlinear Analysis 17, 1-10(1991).
15. ELOE P. W. & HENDERSON J., Positive solutions for higher order ordinary differential equations, Electronic J. of Differential Equations 3, 1-8(1995).
16. ELOE P. W. & HENDERSON J., Positive solutions for (n - 1, 1) boundary value problems, Nonlinear Analysis, to appear.
17. ELOE P. W., HENDERSON J. & WONG P. J. Y., Positive solutions for two-point boundary value problems, in Dynamic Systems and Applications, Vol 2, (edited by G. S. LADDE and M. SAMBANDHAM), to appear.
18. ERBE L. H. & WANG H., On the existence of positive solutions of ordinary differential equations, Proc. Amer. Math. Soc. 120, 743-748(1994).
19. FINK A. M., GATICA J. A. & HERNANDEZ G. E., Eigenvalues of generalized Gel'fand models, Nonlinear Analysis 20, 1453-1468(1993).
20. FINK A. M. & GATICA J. A., Positive solutions of systems of second order boundary value problems, J. Math. Anal. Appl., to appear.
21. v, Bull. Amer. Math. Soc. 75, 132-135(1969).
22. GARAIZAR X., Existence of positive radial solutions for semilinear elliptic problems in the annulus, J. Diff. Eqns. 70, 69-72(1987).
23. GATICA J. A., OLIKER V. & WALTMAN P., Singular nonlinear boundary value problems for second-order ordinary differential equations, J. Diff. Eqs. 79, 62-78(1989).
24. GEL'FAND I. M., Some problems in the theory of quasilinear equations, Uspehi Mat. Nauka 14, 87-158(1959); English translation, Trans. Amer. Math. Soc. 29, 295-381(1963).
25. GEL'FAND I. M., Some problems in the theory of quasilinear equations, Uspehi Mat. Nauka 14, 87-158(1959); English translation, Trans. Amer. Math. Soc. 29, 295-381(1963).
26. HENDERSON J., Singular boundary value problems for difference equations, Dynamic Systems and Applications 1, 271-282(1992).
27. HENDERSON J., Singular boundary value problems for higher order difference equations, in Proc. 1st World Congress of Nonlinear Analysts (Edited by V. LAKSHMIKANTHAM), pp. 1139-1150. Walter de Gruyter and Co., Berlin(1996).
28. KRASNOSEL'SKII M. A., Positive Solutions of Operator Equations, Noordhoff, Groningen(1964).
29. O'REGAN D., Theory of Singular Boundary Value Problems, World Scientific, Singapore(1994).
30. PARTER S., Solutions of differential equations arising in chemical reactor processes, SIAM J. Appl. Math. 26, 687-716(1974).
31. WANG H., On the existence of positive solutions for semilinear elliptic equations in the annulus, J. Diff. Eqns. 109, 1-7(1994).
32. WONG P. J. Y. & AGARWAL R. P., On the existence of solutions of singular boundary value problems for higher order difference equations, Nonlinear Analysis, to appear.
33. WONG P. J. Y. & AGARWAL R. P., On the existence of positive solutions of higher order difference equations, Topological Methods in Nonlinear Analysis, to appear.
34. WONG P. J. Y. & AGARWAL R. P., On the eigenvalues of boundary value problems for higher order difference equations, Rocky Mountain J. Math., to appear.
35. WONG P. J. Y. & AGARWAL R. P., Eigenvalues of boundary value problems for higher order differential equations, Mathematical Problems in Engineering 2, 401-434 (1996).
36. WONG P. J. Y. & AGARWAL R. P., Eigenvalue characterization for (n, p) boundary value problems, J. Austral. Math. Soc. Ser. B, to appear.
37. WONG P. J. Y. & AGARWAL R. P., Eigenvalues of an nth order difference equation with (n, p) type conditions, Dynamics of Continuous, Discrete and Impulsive Systems, to appear.