Positive solutions to singular semi-positone second order dynamic systems
Abstract
By employing the Schauder's xed point theorem, we study theexistence of positive solutions for a singular semipositone dynamic system on time scales. New existence results are established, which is in essence different from the known results.
References
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[2] D. R. Anderson and C. Zhai. Positive solutions to semi-positone second-order three-point problems on time scales. Appl. Math. Comput., 215(10)(2010), 3713-3720.
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[8] E. Cetin and S. G. Topal. Existence of multiple positive solutions for the system of higher order boundary value problems on time scales. Math. Comput. Modelling, 52(1-2)(2010), 1-11.
[9] A. Denk and S. G. Topal. Existence of positive solutions for the second order semipositone m-point boundary value problem. Differ. Equ. Dyn. Syst., 22(3)(2014), 265-280.
[10] M. Joao, L. Sebastian and U. Pedro. Local superlinearity for elliptic system involving parameters. J. Diff. Equat., 211(1)(2005), 1-19.
[11] R. Ma. Multiple nonnegative solutions of second-order systems of boundary value problems. Nonlinear Anal., 42(6)(2000) 1003-1010.
[12] W.T. Li and H.R. Sun. Multiple positive solutions for nonlinear dynamical systems on a measure chain. J. Comput. Appl. Math., 162(2)(2004), 421-430.
[13] Y. Liu and B. Yan. Multiple solutions of singular boundary value problems for differential systems. J. Math. Anal. Appl., 287(2)(2003), 540-556.
[14] L. Liu, X. Zhang and Y.Wu. On existence of positive solutions of a two-point boundary value problem for a nonlinear singular semipositone system. Appl. Math. Comput., 192(1)(2007), 223-232.
[15] 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. Proc. Indian Acad. Sci.(Math. Sci.), 124(1)(2014), 67-79.
[16] H. Wang. On the number of positive solutions of nonlinear systems. J. Math. Anal. Appl., 281(1)(2003), 287-306.
[17] Y. Yang and F. Meng. Positive solutions for the singular semipositone boundary value problem on time scales. Math. Comput. Modelling, 52(3-4)(2010), 481-489.
[18] I. Y. Karaca. Multiple positive solutions for dynamic m-point boundary value problems. Dynamic Systems and Applications, 17 (2008), 25-42.
[19] Y. Zhou and Y. Xu. Positive solutions of three-point boundary value problems for systems of nonlinear second order ordinary differential equations. J. Math. Anal. Appl., 320(2)(2006), 578-590.
[20] X. Zhang, L. Liu and C.Wu. Nontrivial solution of third-order nonlinear eigenvalue problems. Appl. Math. Comput., 176(2)(2006), 714-721.
[21] J. Zhao, H. Lian and W. Ge. Existence of positive solutions for nonlinear m -point boundary value problems on time scales. Boundary Value Problems, 2012 2012:4 DOI: 10.1186/1687-
2770-2012-4.
[2] D. R. Anderson and C. Zhai. Positive solutions to semi-positone second-order three-point problems on time scales. Appl. Math. Comput., 215(10)(2010), 3713-3720.
[3] R. Aris. Introduction to the Analysis of Chemical Reactors. Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1965.
[4] N.A. Asif and R.A. Khan. Positive solutions to singular system with four-point coupled boundary conditions. J. Math. Anal. Appl., 386(2)(2012), 848-861.
[5] M. Bohner A. Peterson. Dynamic Equations on Time Scales, An Introduction with Appli-cations. Birkhauser, Boston, 2001.
[6] M. Bohner and A. Peterson (Eds.). Advances in Dynamic Equations on Time Scales. Birkhfiauser, Boston, 2003.
[7] Z. Cao, Y. Lv, D. Jiang and L. Zu. Positive solutions to singular semipositone boundary value problems of second order coupled differential systems. J. Appl. Math. Comput., 6(1)(2014),
1-16.
[8] E. Cetin and S. G. Topal. Existence of multiple positive solutions for the system of higher order boundary value problems on time scales. Math. Comput. Modelling, 52(1-2)(2010), 1-11.
[9] A. Denk and S. G. Topal. Existence of positive solutions for the second order semipositone m-point boundary value problem. Differ. Equ. Dyn. Syst., 22(3)(2014), 265-280.
[10] M. Joao, L. Sebastian and U. Pedro. Local superlinearity for elliptic system involving parameters. J. Diff. Equat., 211(1)(2005), 1-19.
[11] R. Ma. Multiple nonnegative solutions of second-order systems of boundary value problems. Nonlinear Anal., 42(6)(2000) 1003-1010.
[12] W.T. Li and H.R. Sun. Multiple positive solutions for nonlinear dynamical systems on a measure chain. J. Comput. Appl. Math., 162(2)(2004), 421-430.
[13] Y. Liu and B. Yan. Multiple solutions of singular boundary value problems for differential systems. J. Math. Anal. Appl., 287(2)(2003), 540-556.
[14] L. Liu, X. Zhang and Y.Wu. On existence of positive solutions of a two-point boundary value problem for a nonlinear singular semipositone system. Appl. Math. Comput., 192(1)(2007), 223-232.
[15] 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. Proc. Indian Acad. Sci.(Math. Sci.), 124(1)(2014), 67-79.
[16] H. Wang. On the number of positive solutions of nonlinear systems. J. Math. Anal. Appl., 281(1)(2003), 287-306.
[17] Y. Yang and F. Meng. Positive solutions for the singular semipositone boundary value problem on time scales. Math. Comput. Modelling, 52(3-4)(2010), 481-489.
[18] I. Y. Karaca. Multiple positive solutions for dynamic m-point boundary value problems. Dynamic Systems and Applications, 17 (2008), 25-42.
[19] Y. Zhou and Y. Xu. Positive solutions of three-point boundary value problems for systems of nonlinear second order ordinary differential equations. J. Math. Anal. Appl., 320(2)(2006), 578-590.
[20] X. Zhang, L. Liu and C.Wu. Nontrivial solution of third-order nonlinear eigenvalue problems. Appl. Math. Comput., 176(2)(2006), 714-721.
[21] J. Zhao, H. Lian and W. Ge. Existence of positive solutions for nonlinear m -point boundary value problems on time scales. Boundary Value Problems, 2012 2012:4 DOI: 10.1186/1687-
2770-2012-4.
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2018-01-08
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