American Institute of Mathematical Sciences

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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

Johnny Henderson 1, and  Rodica Luca 2,

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.
Keywords: Second-order di fferential system, positive solutions., integral boundary conditions.
Mathematics Subject Classification: Primary: 34B10; Secondary: 34B1.
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. 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), 75-99. 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(21) (2012), 10572-10585. 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, No. 70 (2013), pp. 1-21. 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(3) (2013), 1035-1054. 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(2) (2013), 233-245. 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), 197-208. Google Scholar

[8]

R. Ma and B. Thompson, Positive solutions for nonlinear $m$-point eigenvalue problems, J. Math. Anal. Appl., 297 (2004), 24-37. 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), 1234-1243. 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), 578-590. Google Scholar

show all references

References:
[1]

H. Amann, Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces, SIAM Review, 18 (1976), 620-709. 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), 75-99. 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(21) (2012), 10572-10585. 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, No. 70 (2013), pp. 1-21. 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(3) (2013), 1035-1054. 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(2) (2013), 233-245. 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), 197-208. Google Scholar

[8]

R. Ma and B. Thompson, Positive solutions for nonlinear $m$-point eigenvalue problems, J. Math. Anal. Appl., 297 (2004), 24-37. 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), 1234-1243. 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), 578-590. Google Scholar

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