Research Article
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On Existence of Symmetric Positive Solutions for SSBVPs on Time Scales

Year 2021, Issue: 37, 86 - 98, 31.12.2021
https://doi.org/10.53570/jnt.1036239
https://izlik.org/JA65KF72GC

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.

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.

Year 2021, Issue: 37, 86 - 98, 31.12.2021
https://doi.org/10.53570/jnt.1036239
https://izlik.org/JA65KF72GC

Abstract

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.
There are 19 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Cansel Kuyumcu 0000-0002-2499-4017

Erbil Çetin 0000-0002-3785-7011

Submission Date December 13, 2021
Publication Date December 31, 2021
DOI https://doi.org/10.53570/jnt.1036239
IZ https://izlik.org/JA65KF72GC
Published in Issue Year 2021 Issue: 37

Cite

APA Kuyumcu, C., & Çetin, E. (2021). On Existence of Symmetric Positive Solutions for SSBVPs on Time Scales. Journal of New Theory, 37, 86-98. https://doi.org/10.53570/jnt.1036239
AMA 1.Kuyumcu C, Çetin E. On Existence of Symmetric Positive Solutions for SSBVPs on Time Scales. JNT. 2021;(37):86-98. doi:10.53570/jnt.1036239
Chicago Kuyumcu, Cansel, and Erbil Çetin. 2021. “On Existence of Symmetric Positive Solutions for SSBVPs on Time Scales”. Journal of New Theory, nos. 37: 86-98. https://doi.org/10.53570/jnt.1036239.
EndNote Kuyumcu C, Çetin E (December 1, 2021) On Existence of Symmetric Positive Solutions for SSBVPs on Time Scales. Journal of New Theory 37 86–98.
IEEE [1]C. Kuyumcu and E. Çetin, “On Existence of Symmetric Positive Solutions for SSBVPs on Time Scales”, JNT, no. 37, pp. 86–98, Dec. 2021, doi: 10.53570/jnt.1036239.
ISNAD Kuyumcu, Cansel - Çetin, Erbil. “On Existence of Symmetric Positive Solutions for SSBVPs on Time Scales”. Journal of New Theory. 37 (December 1, 2021): 86-98. https://doi.org/10.53570/jnt.1036239.
JAMA 1.Kuyumcu C, Çetin E. On Existence of Symmetric Positive Solutions for SSBVPs on Time Scales. JNT. 2021;:86–98.
MLA Kuyumcu, Cansel, and Erbil Çetin. “On Existence of Symmetric Positive Solutions for SSBVPs on Time Scales”. Journal of New Theory, no. 37, Dec. 2021, pp. 86-98, doi:10.53570/jnt.1036239.
Vancouver 1.Kuyumcu C, Çetin E. On Existence of Symmetric Positive Solutions for SSBVPs on Time Scales. JNT [Internet]. 2021 Dec. 1;(37):86-98. Available from: https://izlik.org/JA65KF72GC


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