An application of topological transversality to non-positive higher order difference equations

Applied Mathematics and Computation

Volumn 99, Issue 2-3, 1999, Pages 167-178

  Agarwal, Ravi P ^a   Wong, Fu Hsiang ^b  

^a NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

^b National Taipei Teacher's College   (Taiwan)

Author keywords

A priori bounds; Difference equations; Fixed point; Non positive higher order boundary value problem; Operator equation; Positive solution

Indexed keywords

EID: 0001114598     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0096-3003(98)00005-8     Document Type: Article

References (41)

1. R.P. Agarwal, Difference Equations and Inequalities, Marcel Dekker, New York, 1992.
2. R.P. Agarwal, D. O'Regan, A fixed point approach for nonlinear discrete boundary value problems, Comput. Math. Appl. (to appear).
3. R.P. Agarwal, D. O'Regan, Boundary value problems for discrete equations, Appl. Math. Lett. 10 (4) (1997) 83-89.
4. R.P. Agarwal, F.H. Wong, Existence of positive solutions for higher order boundary value problems, Nonlinear Studies (to appear).
5. R.P. Agarwal, F.H. Wong, Existence of positive solutions for higher order difference equations, Appl. Math. Lett. 10 (5) (1997) 67-74.
6. R.P. Agarwal, F.H. Wong, W.C. Lian, Existence of positive solutions of nonlinear second order differential systems, Appl. Anal. 63 (1996) 375-387.
7. R.P. Agarwal, P.J.Y. Wong, Advanced Topics in Difference Equations, Kluwer Academic Publishers, Dordrecht, 1997.
8. V. Anuradha, D.D. Hai, R. Shivaji, Existence results for superlinear semipositive BVP's, Proc. Amer. Math. Soc. 124 (1996) 757-763.
9. D. Aronson, M.G. Crandall, L.A. Peletier, Stabilization of solutions of a degenerate nonlinear diffusion problem, Nonlinear Anal. 6 (1982) 1001-1022.
10. C. Bandle, C.V. Coffman, M. Marcus, Nonlinear elliptic problems in annular domains, J. Differential Equations 69 (1987) 322-345.
11. C. Bandle, M.K. Kwong, Semilinear elliptic problems in annular domains, J. Appl. Math. Phys. 40 (1989) 245-257.
12. A. Castro, R. Shivaji, Nonnegative solutions for a class of nonpositive problems, Proc. Roy. Edinburgh Soc. Sec. A 108 (1988) 291-302.
13. Y.S. Choi, G.S. Ludford, An unexpected stability result of the near-extinction diffusion flame for non-unity Lewis numbers, Q. J. Mech. Appl. Math. 42 (1) (1989) 143-158.
14. C.J. Chyan, J. Henderson, Positive solutions for singular higher order nonlinear equations, Diff. Eqs. Dyn. Sys. 2 (1994) 153-160.
15. D.S. Cohen, Multiple stable solutions of nonlinear boundary value problems arising in chemical reactor theory, SIAM J. Appl. Math. 20 (1971) 1-13.
16. C.V. Coffman, M. Marcus, Existence and uniqueness results for semilinear Dirichlet problems in annuli, Arch. Rational Mech. Anal. 108 (1989) 293-307.
17. E.N. Dancer, On the structure of solutions of an equation in catalysis theory when a parameter is large, J. Differential Equations 37 (1980) 404-437.
18. D. O'Regan, Theory of Singular Boundary Value Problems, World Scientific, Singapore, 1994.
19. H. Dang, K. Schmitt, Existence of positive solutions for semilinear elliptic equations in annular domain, J. Differential Integral Equations 7 (1994) 747-758.
20. L.H. Erbe, Existence of solutions to boundary value problems for second order differential equations, Nonlinear Anal. 6 (1982) 1155-1162.
21. L.H. Erbe, S. Hu, H. Wang, Multiple positive solutions of some boundary value problems, J. Math. Anal. Appl. 184 (1994) 640-648.
22. L.H. Erbe, H. Wang, On the existence of positive solutions of ordinary differential equations, Proc. Amer. Math. Soc. 120 (1994) 743-748.
23. X. Garaizar, Existence of positive radial solutions for semilinear elliptic equations in the annulus, J. Differential Equations 70 (1987) 69-72.
24. A. Granas, R.B. Guenther, J.W. Lee, On a theorem of S, Bernstein, Pacific J. Math. 73 (1977) 1-16.
25. A. Granas, R.B. Guenther, J.W. Lee, Nonlinear boundary value problems for some classes of ordinary differential equations, Rocky Mount. J. Math. 10 (1980) 35-38.
26. G.B. Gustafson, K. Schmitt, Nonzero solutions of boundary value problems for second order ordinary and delay-differential equations, J. Differential Equations 12 (1972) 127-147.
27. J. Henderson, Singular boundary value problems for difference equations, Dynamic Systems Applications 1 (1992) 271-282.
28. G. Iffland, Positive solutions of a problem of Emden-Fowler type with a free boundary, SIAM J. Math. Anal. 18 (1987) 283-292.
29. P. Kelevedjiev, Existence of solutions for two-point boundary value problems, Nonlinear Anal. 22 (1994) 217-224.
30. P. Kelevedjiev, Nonexistence of solutions for two-point boundary value problems, Nonlinear Anal. 22 (1994) 225-228.
31. J.W. Lee, D. O'Regan, Nonlinear boundary value problems in Hilbert spaces, J. Math. Anal. Appl. 137 (1989) 59-69.
32. J. Mawhin, Topological degree and boundary value problems for nonlinear differential equations, NSFCB Regional Conference Series in Math, vol. 40, American Mathematical Society, Providence, RI, 1979.
33. J. Santanilla, Nonnegative solutions to boundary value problems for nonlinear first and second order ordinary differential equations, J. Math. Anal. Appl. 126 (1987) 397-408.
34. A. Tineo, A comparison theorem for second order ODEs and applications to singular problems, J. Differential Equations 116 (1995) 16-30.
35. H. Wang, On the existence of positive solutions for semilinear elliptic equations in the annulus, J. Differential Equations 109 (1994) 1-7.
36. F.H. Wong, Existence of positive solutions of singular boundary value problems, Nonlinear Anal. 21 (1993) 397-406.
37. F.H. Wong, S.L. Yu, Uniqueness of positive solutions for singular nonlinear boundary value problems, Hiroshima Math. J. 26 (1996) 233-243.
38. P.J.Y. Wong, R.P. Agarwal, Eigenvalues of boundary value problems for higher order differential equations, Math. Probl. Eng. 2 (1996) 401-434.
39. P.J.Y. Wong, R.P. Agarwal, 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. Meth. Nonlinear Anal, (to appear).
41. P.J.Y. Wong, R.P. Agarwal, On the eigenvalues of boundary value problems for higher order difference equations, Rocky Mountain J. Math, (to appear).