S. Gülşan TOPAL

Second-Order Nonlinear Three Point Boundary-Value Problems on Time Scales

We consider a second order three point boundary value problem for dynamic equations on time scales and establish criteria for the existence of at least two positive solutions of an eigenvalue problem by an application of a fixed point theorem in cones. Existence result for non-eigenvalue problem is also given by the monotone method.

Anahtar Kelimeler:

Dynamic equations, cone, positive solutions, upper and lower solutions

Second-Order Nonlinear Three Point Boundary-Value Problems on Time Scales

Keywords:

Dynamic equations, cone, positive solutions, upper and lower solutions,

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R.P. Agarwal, M. Bohner, Basic calculus on time scales and some of its applications, Results Math., 35(1-2), 3-22,1999.
D. R. Anderson, Solutions to second-order three-point problems on time scales, J. Difference Equ. Appl., 8, 673-688, 2002.
D. R. Anderson and R. I. Avery, An even-order three-point problems on time scales, J. Math. Anal. Appl., 291, 514-525, 2004.
F. Merdivenci Atici and A. Cabada, The method of upper and lower solutions for discrete second order periodic boundary value problems, Comput. Math. Appl., 45, 1417-1427, 2003.
F. Merdivenci Atici and G. Sh. Guseinov, On Green’s functions and positive solutions for baundary value problems on time scales, J. Comput. Appl. Math., 141(1-2), 75-99, 2002.
F. Merdivenci Atici and S. G. Topal, Nonlinear three point baundary value problems on time scales, Dynamic Systems Appl., 13, 327-337, 2004.
M. Bohner and A. Peterson, Dynamic Equations on time scales, An Introduction with Applications , Birkh¨auser, 2001.
M. Bohner and A. Peterson, Advances in Dynamic Equations on Time Scales, Birkh¨auser, Boston, 2003.
D. Guo, V. Lakshmikantham, Nonlinear Problems in Abstract Cones, Academic Press, San Diego, 1988.
C.P. Gupta, Solvability of a three-point nonlinear boundary value problem under for a second order ordinary differential equation, J. Math. Anal. Appl., 168, 540551, 1992.
C.P. Gupta, A sharper condition for solvability of a three-point nonlinear boundary value problem, J. Math. Anal. Appl., 205, 586597, 1997.
E. R. Kaufmann, Positive solutions of a three-point boundary value problem on time scale Electronic J. Diff. Equ., 82, 1-11, 2003.
B. Liu, Positive solutions of a nonlinear three-point boundary value problem, Appl. Math. and Computation, 132, No: 1, 11-28, 2002.
R. Ma, Positive solutions of a nonlinear three-point boundary-value problem, Electronic Journal of Differential Equations, 34, 1-8, 1998.
R. Ma, Positive solutions for second-order three-point boundary-value problems, Applied Mathematics Letters, 14, 1-5, 2001. S. G¨ul¸san TOPAL
Department of Mathematics, Ege University, Bornova, ˙Izmir-TURKEY e-mail: stopal@sci.ege.edu.tr