In this paper, we study the existence of coupled solutions of anti-periodic boundary value problems for impulsive differential equations with ϕ-Laplacian operator. Based on a pair of coupled lower and upper solutions and appropriate Nagumo condition, we prove the existence of coupled solutions for anti-periodic impulsive differential equations boundary value problems with ϕ-Laplacian operator.
Published in | Science Journal of Applied Mathematics and Statistics (Volume 4, Issue 6) |
DOI | 10.11648/j.sjams.20160406.18 |
Page(s) | 298-302 |
Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
Copyright |
Copyright © The Author(s), 2016. Published by Science Publishing Group |
Boundary Value Problems, Coupled Solutions, Impulsive Differential Equations, ϕ-Laplacian Operator
[1] | C. Ahn, C. Rim, Boundary flows in general coset theories, J. Phys. A 32 (1999) 2509-2525. |
[2] | D. Bainov, V. Covachev, Impulsive Differential Equations With a Small Parameter, World Scientific, Singapore, 1994. |
[3] | M. Benchohra, J. Henderson, S. K. Ntouyas, Impulsive Differential Equations and Inclusions, Hindawi Publishing Corparation, New York, 2006. |
[4] | H. L. Chen, Antiperiodic wavelets, J. Comput. Math. 14 (1996) 32-39. |
[5] | A. Cabada, D. R. Vivero, Existence and uniqueness of solutions of higher-order antiperiodic dynamic equations, Adv. Difference Equ. 4 (2004) 291-310. |
[6] | A. Cabada, The method of lower and upper solutions for periodic and anti-periodic difference quations, Electron. Trans. Numer. Anal. 27 (2007) 13-25. |
[7] | A. Cabada, An overview of the lower and upper solutions method with nonlinear boundary value conditions, Bound. Value Probl.(2011)18. Art. ID 893753. |
[8] | Y. Chen, J. J. Nieto, D. O’Regan, Anti-periodic solutions for fully nonlinear first-order differential equations, Math. Comput. Model. 46 (2007) 1183-1190. |
[9] | Y. Chen, J. J. Nieto, D. O’Regan, Anti-periodic solutions for evolution equations associated with maximal monotone mappings, Appl. Math. Lett. 24 (2011) 302-307. |
[10] | E. N. Dancer. On the Dirichlet problem for weakly non-linear elliptic partial differential equations. Proc. Roy. Soc. Edinburgh Sect. A, 76 (1977) 283-300. |
[11] | F. J. Delvos, L. Knoche, Lacunary interpolation by anti-periodic trigonometric polynomials, BIT 39 (1999) 439-450. |
[12] | X. Guo, L. Lu, Z. Liu, BVPs for higher-order integro-differential equations with ϕ-Laplacian and functional boundary conditions, Adv. Differ. Equa. 2014:285 (2014) 1-13. |
[13] | H. Kleinert, A. Chervyakov, Functional determinants from Wronski Green function, J. Math. Phys. 40 (1999) 6044-6051. |
[14] | V. Lakshmikantham, D. D. Bainov, P. S. Simeonov, Theory of Impulsive Differential Equations, World Scientific, Singapore, 1989. |
[15] | S. P. Lu, Periodic solutions to a second order -Laplacian neutral functional differential system, Nonlinear Anal. 69 (2008) 4215-4229. |
[16] | Z. Luo, J. J. Nieto, New results of periodic boundary value problem for impulsive integro-differential equations, Nonlinear Anal. 70 (2009) 2248-2260. |
[17] | H. Okochi, On the existence of periodic solutions to nonlinear abstract parabolic equations, J. Math. Soc. Japan 40(3) (1988) 541-553. |
[18] | K. Perera, R. P. Agarwal, D. O’Regan, Morse Theoretic Aspects of -Laplacian Type Operators, American Mathematical Society, Providence, Rhode Island, 2010. |
[19] | W. Wang, J. Shen, Existence of solutions for anti-periodic boundary value problems, Nonlinear Anal. 70 (2009) 598-605. |
[20] | R. Wu, The existence of -anti-periodic solutions, Appl. Math. Lett. 23 (2010) 984-987. |
[21] | M. P. Yao, A. M. Zhao, J. R. Yan, Anti-periodic boundary value problems of second order impulsive differential equations, Comp. Math. Appl. 59 (2010) 3617-362. |
[22] | X. F. Guo, Y. Gu, Anti-periodic Boundary Value Problems of -Laplacian Impulsive Differential Equations, Appl. Comput. Math. 5(2) (2016) 91-96. |
[23] | A. Cabada, J. Tomecek, Extremal solutions for nonlinear functional ϕ-Laplacian impulsive equations, Nonlinear Anal. 67(2007)827-841. |
[24] | M. Wang, A. Cabada, J. J. Nieto, Monotone method for nonlinear second order periodic boundary value problems with Caratheodory functions, Ann. Polon. Math. 58(3) (1993) 221-235. |
[25] | J. F. Xu, Z. L. Yang, Positive solutions for a fourth order -Laplacian boundary value problem, Nonlinear Anal. 74 (2011) 2612-2623. |
APA Style
Xiufeng Guo. (2016). Existence of Coupled Solutions of BVP for ϕ-Laplacian Impulsive Differential Equations. Science Journal of Applied Mathematics and Statistics, 4(6), 298-302. https://doi.org/10.11648/j.sjams.20160406.18
ACS Style
Xiufeng Guo. Existence of Coupled Solutions of BVP for ϕ-Laplacian Impulsive Differential Equations. Sci. J. Appl. Math. Stat. 2016, 4(6), 298-302. doi: 10.11648/j.sjams.20160406.18
AMA Style
Xiufeng Guo. Existence of Coupled Solutions of BVP for ϕ-Laplacian Impulsive Differential Equations. Sci J Appl Math Stat. 2016;4(6):298-302. doi: 10.11648/j.sjams.20160406.18
@article{10.11648/j.sjams.20160406.18, author = {Xiufeng Guo}, title = {Existence of Coupled Solutions of BVP for ϕ-Laplacian Impulsive Differential Equations}, journal = {Science Journal of Applied Mathematics and Statistics}, volume = {4}, number = {6}, pages = {298-302}, doi = {10.11648/j.sjams.20160406.18}, url = {https://doi.org/10.11648/j.sjams.20160406.18}, eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20160406.18}, abstract = {In this paper, we study the existence of coupled solutions of anti-periodic boundary value problems for impulsive differential equations with ϕ-Laplacian operator. Based on a pair of coupled lower and upper solutions and appropriate Nagumo condition, we prove the existence of coupled solutions for anti-periodic impulsive differential equations boundary value problems with ϕ-Laplacian operator.}, year = {2016} }
TY - JOUR T1 - Existence of Coupled Solutions of BVP for ϕ-Laplacian Impulsive Differential Equations AU - Xiufeng Guo Y1 - 2016/12/14 PY - 2016 N1 - https://doi.org/10.11648/j.sjams.20160406.18 DO - 10.11648/j.sjams.20160406.18 T2 - Science Journal of Applied Mathematics and Statistics JF - Science Journal of Applied Mathematics and Statistics JO - Science Journal of Applied Mathematics and Statistics SP - 298 EP - 302 PB - Science Publishing Group SN - 2376-9513 UR - https://doi.org/10.11648/j.sjams.20160406.18 AB - In this paper, we study the existence of coupled solutions of anti-periodic boundary value problems for impulsive differential equations with ϕ-Laplacian operator. Based on a pair of coupled lower and upper solutions and appropriate Nagumo condition, we prove the existence of coupled solutions for anti-periodic impulsive differential equations boundary value problems with ϕ-Laplacian operator. VL - 4 IS - 6 ER -