Cansel KUYUMCU, Erbil ÇETİN

On the Existence of Symmetric Positive Solutions for SSBVPs on Time Scales

This paper considers symmetric positive solutions for the system of second-order boundary value problems (SSBVPs) on time scales using the Krasnosel’skii fixed point theorem. We then demonstrate two examples. Finally, we discuss the need for further results.

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1] S. Hilger, Ein Masskettenkalkül mit Anwendug auf zentrumsmanningfaltigkeiten, PhD Dissertation, Universitat Würzburg (1988) Germany.
[2] F. M. Atıcı, D. C. Biles, A. Lebedinsky, An Application of Time Scales to Economics, Mathematical and Computer Modelling 43 (2006) 718–726.
[3] M. A. Jones, B. Song, D. M. Thomas, Controlling Wound Healing Through Debridement, Mathematical and Computer Modelling 40 (2004) 1057–1064.
[4] V. Spedding, Taming Nature’s Numbers, New Scientist (2003) 28–32.
[5] D. M. Thomas, L. Vandemuelebroeke, K. Yamaguchi, A Mathematical Evolution Model for Phytoremediation of Metals, Discrete and Continuous Dynamical Systems Series B 5(2) (2005) 411–422.
[6] H. Qu, The Symmetric Positive Solutions of Four-point Problems for Nonlinear Boundary Value Secondorder Differential Equations, International Journal of Mathematical Analysis, 3(40) (2009) 1969–1979.
[7] J. Henderson and H. B. Thompson, Multiple Symmetric Positive Solutions for a Second Order Boundary Value Problem, Proceedings of the American Mathematical Society 128 (2000) 2373–2379.
[8] F. Li, Y. Zhang, Multiple Symmetric Nonnegative Solutions of Second-order Ordinary Differential Equations, Applied Mathematics Letters 17 (2004) 261–267.,
[9] Q. Yao, Existence and Iteration of ? Symmetric Positive Solutio ns for a Singular Two-point Boundary Value Problem, Computers & Mathematics with Applications 47 (2004) 1195–1200.
[10] Y. P. Sun, Existence and Multiplicity of Symmetric Positive Solutions for Three-point Boundary Value Problem, Applied Mathematics Letters 329 (2007) 998–1009.
[11] N. A. Hamal, F. Yoruk, Symmetric Positive Solutions of Fourth Order Integral BVP for an Increasing Homeomorphism and Homomorphism with Sign-changing Nonlinearity on Time Scales, Computers & Mathematics with Applications 59(11) (2010) 3603–3611.
[12] E. Cetin, F. S. Topal, Symmetric Positive Solutions of Fourth Order Boundary Value Problems for an Increasing Homeomorphism and Homomorphism on Time Scales, Computers and Mathematics with Applications, 63(3) (2012) 669–678.
[13] K. R. Prasad, A. K. Rao and B. Bharathi, Positive Solutions for System of 2n-th Order Sturm–Liouville Boundary Value Problems on Time Scales, Proceedings of the Indian Academy of Sciences: Mathematical Sciences 124 (2014), 67–79.
[14] A. D. Oğuz, F. S. Topal, Symmetric Positive Solutions for the Systems of Higher-order Boundary Value Problems on Time Scales, Advances in Pure and Applied Mathematics 8(4) (2017) 285–292.
[15] M. Bohner, A. Peterson, Dynamic Equations on Time Scales, An Introduction with Applications, Birkhäuser, Boston, 2001.
[16] M. Bohner, A. Peterson, (Eds.), Advances in Dynamic Equations on Time Scales, Birkhäuser, Boston, 2003.
[17] S. Hilger, Analysis on Measure Chains-A Unified Approach to Continuous and Discrete Calculus, Results in Mathematics 18 (1990) 18–56.
[18] M. Krasnosel’skii, Positive Solutions of Operator Equations, Noordhoff, Groningen, 1964.
[19] F. Deimling, Nonlinear Functional Analysis, Springer, NewYork, 1985.