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Triple solutions to boundary value problems on time scales. (English) Zbl 0958.34021
Using the Leggett-Williams fixed-point theorem, three nonnegative solutions are proved to nonlinear differential equations on time scales. The obtained result is new for differential equations as well as discrete particular cases.

34B18Positive solutions of nonlinear boundary value problems for ODE
34B15Nonlinear boundary value problems for ODE
34A99General theory of ODE
Full Text: DOI
[1] Agarwal, R. P.; Bohner, M.: Basic calculus on time scales and some of its applications. Results in mathematics 35, 3-22 (1999) · Zbl 0927.39003
[2] Agarwal, R. P.; Bohner, M.; Wong, P.: Sturm-Liouville eigenvalue problems on time scales. Applied mathematics and computation 99, 153-166 (1999) · Zbl 0938.34015
[3] R.P. Agarwal and D. O’Regan, Nonlinear boundary value problems on time scales, Nonlinear Analysis (to appear).
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[10] Leggett, R. W.; Williams, L. R.: Multiple positive fixed points of nonlinear operators on ordered Banach spaces. Indiana math. J. 28, 673-688 (1979) · Zbl 0421.47033
[11] Agarwal, R. P.; O’regan, D.; Wong, P. J. Y.: Positive solutions of differential, difference and integral equations. (1999)
[12] Anderson, D.; Avery, R. I.; Peterson, A. C.: Three positive solutions to a discrete focal boundary value problem. J. comput. Appl. math. 88, 103-118 (1998) · Zbl 1001.39021
[13] P.J. Wong and R.P. Agarwal, Criteria for multiple solutions of difference and partial difference equations subject to multipoint conjugate conditions, Nonlinear Analysis (to appear). · Zbl 0959.39002