# 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.   Google Scholar [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.   Google Scholar [3] J. Henderson and R. Luca, Existence and multiplicity for positive solutions of a multi-point boundary value problem,, Appl. Math. Comput., 218 (2012), 10572.   Google Scholar [4] J. Henderson and R. Luca, Positive solutions for systems of second-order integral boundary value problems,, Electr. J. Qual. Theory Diff. Equ., 2013 (2013), 1.   Google Scholar [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 (2013), 1035.   Google Scholar [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 (2013), 233.   Google Scholar [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.   Google Scholar [8] R. Ma and B. Thompson, Positive solutions for nonlinear $m$-point eigenvalue problems,, J. Math. Anal. Appl., 297 (2004), 24.   Google Scholar [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.   Google Scholar [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.   Google Scholar

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##### References:
 [1] H. Amann, Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces,, SIAM Review, 18 (1976), 620.   Google Scholar [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.   Google Scholar [3] J. Henderson and R. Luca, Existence and multiplicity for positive solutions of a multi-point boundary value problem,, Appl. Math. Comput., 218 (2012), 10572.   Google Scholar [4] J. Henderson and R. Luca, Positive solutions for systems of second-order integral boundary value problems,, Electr. J. Qual. Theory Diff. Equ., 2013 (2013), 1.   Google Scholar [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 (2013), 1035.   Google Scholar [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 (2013), 233.   Google Scholar [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.   Google Scholar [8] R. Ma and B. Thompson, Positive solutions for nonlinear $m$-point eigenvalue problems,, J. Math. Anal. Appl., 297 (2004), 24.   Google Scholar [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.   Google Scholar [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.   Google Scholar
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