# American Institute of Mathematical Sciences

2015, 2015(special): 596-604. doi: 10.3934/proc.2015.0596

## Existence of positive solutions for a system of nonlinear second-order integral boundary value problems

 1 Department of Mathematics, Baylor University, Waco, Tx 76798 2 Department of Mathematics, Gh. Asachi Technical University, Iasi 700506, Romania

Received  September 2014 Revised  May 2015 Published  November 2015

We study the existence and multiplicity of positive solutions of a system of nonlinear second-order ordinary differential equations subject to Riemann-Stieltjes integral boundary conditions.
Citation: Johnny Henderson, Rodica Luca. Existence of positive solutions for a system of nonlinear second-order integral boundary value problems. Conference Publications, 2015, 2015 (special) : 596-604. doi: 10.3934/proc.2015.0596
##### References:
 [1] H. Amann, Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces, SIAM Review, 18 (1976), 620-709. [2] F. M. Atici and G. Sh. Guseinov, On Green's functions and positive solutions for boundary value problems on time scales, J. Comput. Appl. Math., 141 (2002), 75-99. [3] J. Henderson and R. Luca, Existence and multiplicity for positive solutions of a multi-point boundary value problem, Appl. Math. Comput., 218(21) (2012), 10572-10585. [4] J. Henderson and R. Luca, Positive solutions for systems of second-order integral boundary value problems, Electr. J. Qual. Theory Diff. Equ., 2013, No. 70 (2013), pp. 1-21. [5] J. Henderson and R. Luca, Existence and multiplicity for positive solutions of a system of higher-order multi-point boundary value problems, Nonlinear Differ. Equ. Appl., 20(3) (2013), 1035-1054. [6] J. Henderson and R. Luca, Existence and multiplicity of positive solutions for a system of higher-order multi-point boundary value problems, Adv. Dyn. Syst. Applic., 8(2) (2013), 233-245. [7] J. Henderson and R. Luca, Positive solutions for a system of second-order nonlinear multi-point eigenvalue problems, Appl. Math. Comput., 223 (2013), 197-208. [8] R. Ma and B. Thompson, Positive solutions for nonlinear $m$-point eigenvalue problems, J. Math. Anal. Appl., 297 (2004), 24-37. [9] H. Su, Z. Wei, X. Zhang and J. Liu, Positive solutions of $n$-order and $m$-order multi-point singular boundary value system, Appl. Math. Comput., 188 (2007), 1234-1243. [10] 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 (2006), 578-590.

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##### References:
 [1] H. Amann, Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces, SIAM Review, 18 (1976), 620-709. [2] F. M. Atici and G. Sh. Guseinov, On Green's functions and positive solutions for boundary value problems on time scales, J. Comput. Appl. Math., 141 (2002), 75-99. [3] J. Henderson and R. Luca, Existence and multiplicity for positive solutions of a multi-point boundary value problem, Appl. Math. Comput., 218(21) (2012), 10572-10585. [4] J. Henderson and R. Luca, Positive solutions for systems of second-order integral boundary value problems, Electr. J. Qual. Theory Diff. Equ., 2013, No. 70 (2013), pp. 1-21. [5] J. Henderson and R. Luca, Existence and multiplicity for positive solutions of a system of higher-order multi-point boundary value problems, Nonlinear Differ. Equ. Appl., 20(3) (2013), 1035-1054. [6] J. Henderson and R. Luca, Existence and multiplicity of positive solutions for a system of higher-order multi-point boundary value problems, Adv. Dyn. Syst. Applic., 8(2) (2013), 233-245. [7] J. Henderson and R. Luca, Positive solutions for a system of second-order nonlinear multi-point eigenvalue problems, Appl. Math. Comput., 223 (2013), 197-208. [8] R. Ma and B. Thompson, Positive solutions for nonlinear $m$-point eigenvalue problems, J. Math. Anal. Appl., 297 (2004), 24-37. [9] H. Su, Z. Wei, X. Zhang and J. Liu, Positive solutions of $n$-order and $m$-order multi-point singular boundary value system, Appl. Math. Comput., 188 (2007), 1234-1243. [10] 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 (2006), 578-590.
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