American Institute of Mathematical Sciences

Advanced
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.

[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.

show all references

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.

[1]

Abdelkader Boucherif. Positive Solutions of second order differential equations with integral boundary conditions. Conference Publications, 2007, 2007 (Special) : 155-159. doi: 10.3934/proc.2007.2007.155
[2]

Qiong Meng, X. H. Tang. Solutions of a second-order Hamiltonian system with periodic boundary conditions. Communications on Pure and Applied Analysis, 2010, 9 (4) : 1053-1067. doi: 10.3934/cpaa.2010.9.1053
[3]

Xiaoping Wang. Ground state homoclinic solutions for a second-order Hamiltonian system. Discrete and Continuous Dynamical Systems - S, 2019, 12 (7) : 2163-2175. doi: 10.3934/dcdss.2019139
[4]

Gennaro Infante. Eigenvalues and positive solutions of odes involving integral boundary conditions. Conference Publications, 2005, 2005 (Special) : 436-442. doi: 10.3934/proc.2005.2005.436
[5]

Eugenii Shustin, Emilia Fridman, Leonid Fridman. Oscillations in a second-order discontinuous system with delay. Discrete and Continuous Dynamical Systems, 2003, 9 (2) : 339-358. doi: 10.3934/dcds.2003.9.339
[6]

Yan Liu, Fei Guo. Multiplicity of periodic solutions for second-order perturbed Hamiltonian systems with local superquadratic conditions. Communications on Pure and Applied Analysis, , () : -. doi: 10.3934/cpaa.2022098
[7]

Daniel Franco, Donal O'Regan. Existence of solutions to second order problems with nonlinear boundary conditions. Conference Publications, 2003, 2003 (Special) : 273-280. doi: 10.3934/proc.2003.2003.273
[8]

Qilin Wang, Xiao-Bing Li, Guolin Yu. Second-order weak composed epiderivatives and applications to optimality conditions. Journal of Industrial and Management Optimization, 2013, 9 (2) : 455-470. doi: 10.3934/jimo.2013.9.455
[9]

Xiaoni Chi, Zhongping Wan, Zijun Hao. Second order sufficient conditions for a class of bilevel programs with lower level second-order cone programming problem. Journal of Industrial and Management Optimization, 2015, 11 (4) : 1111-1125. doi: 10.3934/jimo.2015.11.1111
[10]

Tran Hong Thai, Nguyen Anh Dai, Pham Tuan Anh. Global dynamics of some system of second-order difference equations. Electronic Research Archive, 2021, 29 (6) : 4159-4175. doi: 10.3934/era.2021077
[11]

Jaume Llibre, Amar Makhlouf. Periodic solutions of some classes of continuous second-order differential equations. Discrete and Continuous Dynamical Systems - B, 2017, 22 (2) : 477-482. doi: 10.3934/dcdsb.2017022
[12]

Xuan Wu, Huafeng Xiao. Periodic solutions for a class of second-order differential delay equations. Communications on Pure and Applied Analysis, 2021, 20 (12) : 4253-4269. doi: 10.3934/cpaa.2021159
[13]

Mariane Bourgoing. Viscosity solutions of fully nonlinear second order parabolic equations with $L^1$ dependence in time and Neumann boundary conditions. Discrete and Continuous Dynamical Systems, 2008, 21 (3) : 763-800. doi: 10.3934/dcds.2008.21.763
[14]

Monica Motta, Caterina Sartori. Uniqueness of solutions for second order Bellman-Isaacs equations with mixed boundary conditions. Discrete and Continuous Dynamical Systems, 2008, 20 (4) : 739-765. doi: 10.3934/dcds.2008.20.739
[15]

Huaiyu Zhou, Jingbo Dou. Classifications of positive solutions to an integral system involving the multilinear fractional integral inequality. Discrete and Continuous Dynamical Systems, 2022  doi: 10.3934/dcds.2022070
[16]

Maria Do Rosario Grossinho, Rogério Martins. Subharmonic oscillations for some second-order differential equations without Landesman-Lazer conditions. Conference Publications, 2001, 2001 (Special) : 174-181. doi: 10.3934/proc.2001.2001.174
[17]

Liwei Zhang, Jihong Zhang, Yule Zhang. Second-order optimality conditions for cone constrained multi-objective optimization. Journal of Industrial and Management Optimization, 2018, 14 (3) : 1041-1054. doi: 10.3934/jimo.2017089
[18]

Hongwei Lou, Jiongmin Yong. Second-order necessary conditions for optimal control of semilinear elliptic equations with leading term containing controls. Mathematical Control and Related Fields, 2018, 8 (1) : 57-88. doi: 10.3934/mcrf.2018003
[19]

Hongwei Lou. Second-order necessary/sufficient conditions for optimal control problems in the absence of linear structure. Discrete and Continuous Dynamical Systems - B, 2010, 14 (4) : 1445-1464. doi: 10.3934/dcdsb.2010.14.1445
[20]

Gennaro Infante. Positive solutions of differential equations with nonlinear boundary conditions. Conference Publications, 2003, 2003 (Special) : 432-438. doi: 10.3934/proc.2003.2003.432

 Impact Factor: 

Tools

Metrics

  • PDF downloads (146)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy