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Sign-variations of solutions of nonlinear discrete boundary value problems

Published online by Cambridge University Press:  17 April 2009

Ruyun Ma
Affiliation:
Department of Mathematics, Northwest Normal University, Lanzhou 730070, Peoples Republic ov China e-mail: mary@nwnu.edu.cn
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In this paper, we study two-point boundary value problems for the nonlinear second order difference equation We establish the relationship between the number of sign-variation of f on {0,…, T + 2} and the one of the solution u of the above problem.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2007

References

[1]Agarwal, R.P., Bohner, M. and Wong, P.J.Y., ‘Sturm-Liouville eigenvalue problems on time scales’, Appl. Math. Comput. 99 (1999), 153166.Google Scholar
[2]Bellman, R., ‘On variation-diminishing properties of Green's functions’, Boll. Un. Mat. Ital. (3) 16 (1961), 164166.Google Scholar
[3]Boucherif, A. and Slimani, B.A., ‘On the sign-variations of solutions of nonlinear two-point boundary value problems’, Nonlinear Anal. 22 (1994), 15671577.CrossRefGoogle Scholar
[4]Lazer, A.C. and McKenna, P.J., ‘Global bifurcation and a theorem of Tarantello’, J. Math. Anal. Appl. 181 (1994), 648655.CrossRefGoogle Scholar
[5]Kelley, W.G. and Peterson, A.C., Difference equations (Academic Press, New York, 1991).Google Scholar
[6]Pachpatte, B.G., ‘A note on Opial and Wirtinger type discrete inequalities’, J. Math. Anal. Appl. 127 (1987), 470474.CrossRefGoogle Scholar