On Existence of Symmetric Positive Solutions for SSBVPs on Time Scales

Year 2021, Issue: 37, 86 - 98, 31.12.2021

Cansel Kuyumcu , Erbil Çetin

https://doi.org/10.53570/jnt.1036239

Abstract

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.

Keywords

Time scale, symmetric positive solution, boundary value problem, Krasnosel’skii fixed point theorem

References

• S. Hilger, Ein Masskettenkalkül mit Anwendug auf zentrumsmanningfaltigkeiten, PhD Dissertation, Universitat Würzburg (1988) Germany.
• F. M. Atıcı, D. C. Biles, A. Lebedinsky, An Application of Time Scales to Economics, Mathematical and Computer Modelling 43 (2006) 718–726.
• M. A. Jones, B. Song, D. M. Thomas, Controlling Wound Healing Through Debridement, Mathematical and Computer Modelling 40 (2004) 1057–1064.
• V. Spedding, Taming Nature’s Numbers, New Scientist (2003) 28–32.
• 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.
• H. Qu, The Symmetric Positive Solutions of Four-point Problems for Nonlinear Boundary Value Second-order Differential Equations, International Journal of Mathematical Analysis, 3(40) (2009) 1969–1979.
• 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.
• F. Li, Y. Zhang, Multiple Symmetric Nonnegative Solutions of Second-order Ordinary Differential Equations, Applied Mathematics Letters 17 (2004) 261–267.
• Q. Yao, Existence and Iteration of n Symmetric Positive Solutions for a Singular Two-point Boundary Value Problem, Computers & Mathematics with Applications 47 (2004) 1195–1200.
• Y. P. Sun, Existence and Multiplicity of Symmetric Positive Solutions for Three-point Boundary Value Problem, Applied Mathematics Letters 329 (2007) 998–1009.
• 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.
• 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.
• 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.
• 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.
• M. Bohner, A. Peterson, Dynamic Equations on Time Scales, An Introduction with Applications, Birkhäuser, Boston, 2001.
• M. Bohner, A. Peterson, (Eds.), Advances in Dynamic Equations on Time Scales, Birkhäuser, Boston, 2003.
• S. Hilger, Analysis on Measure Chains-A Unified Approach to Continuous and Discrete Calculus, Results in Mathematics 18 (1990) 18–56.
• M. Krasnosel’skii, Positive Solutions of Operator Equations, Noordhoff, Groningen, 1964.
• F. Deimling, Nonlinear Functional Analysis, Springer, NewYork, 1985.