Existence of Coupled Solutions of BVP for ϕ-Laplacian Impulsive Differential Equations
Science Journal of Applied Mathematics and Statistics
Volume 4, Issue 6, December 2016, Pages: 298-302
Received: Nov. 4, 2016; Accepted: Nov. 25, 2016; Published: Dec. 14, 2016
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Xiufeng Guo, College of Sciences, Hezhou University, Hezhou, China
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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.
Boundary Value Problems, Coupled Solutions, Impulsive Differential Equations, ϕ-Laplacian Operator
To cite this article
Xiufeng Guo, Existence of Coupled Solutions of BVP for ϕ-Laplacian Impulsive Differential Equations, Science Journal of Applied Mathematics and Statistics. Vol. 4, No. 6, 2016, pp. 298-302. doi: 10.11648/j.sjams.20160406.18
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C. Ahn, C. Rim, Boundary flows in general coset theories, J. Phys. A 32 (1999) 2509-2525.
D. Bainov, V. Covachev, Impulsive Differential Equations With a Small Parameter, World Scientific, Singapore, 1994.
M. Benchohra, J. Henderson, S. K. Ntouyas, Impulsive Differential Equations and Inclusions, Hindawi Publishing Corparation, New York, 2006.
H. L. Chen, Antiperiodic wavelets, J. Comput. Math. 14 (1996) 32-39.
A. Cabada, D. R. Vivero, Existence and uniqueness of solutions of higher-order antiperiodic dynamic equations, Adv. Difference Equ. 4 (2004) 291-310.
A. Cabada, The method of lower and upper solutions for periodic and anti-periodic difference quations, Electron. Trans. Numer. Anal. 27 (2007) 13-25.
A. Cabada, An overview of the lower and upper solutions method with nonlinear boundary value conditions, Bound. Value Probl.(2011)18. Art. ID 893753.
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.
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.
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.
F. J. Delvos, L. Knoche, Lacunary interpolation by anti-periodic trigonometric polynomials, BIT 39 (1999) 439-450.
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.
H. Kleinert, A. Chervyakov, Functional determinants from Wronski Green function, J. Math. Phys. 40 (1999) 6044-6051.
V. Lakshmikantham, D. D. Bainov, P. S. Simeonov, Theory of Impulsive Differential Equations, World Scientific, Singapore, 1989.
S. P. Lu, Periodic solutions to a second order -Laplacian neutral functional differential system, Nonlinear Anal. 69 (2008) 4215-4229.
Z. Luo, J. J. Nieto, New results of periodic boundary value problem for impulsive integro-differential equations, Nonlinear Anal. 70 (2009) 2248-2260.
H. Okochi, On the existence of periodic solutions to nonlinear abstract parabolic equations, J. Math. Soc. Japan 40(3) (1988) 541-553.
K. Perera, R. P. Agarwal, D. O’Regan, Morse Theoretic Aspects of -Laplacian Type Operators, American Mathematical Society, Providence, Rhode Island, 2010.
W. Wang, J. Shen, Existence of solutions for anti-periodic boundary value problems, Nonlinear Anal. 70 (2009) 598-605.
R. Wu, The existence of -anti-periodic solutions, Appl. Math. Lett. 23 (2010) 984-987.
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.
X. F. Guo, Y. Gu, Anti-periodic Boundary Value Problems of -Laplacian Impulsive Differential Equations, Appl. Comput. Math. 5(2) (2016) 91-96.
A. Cabada, J. Tomecek, Extremal solutions for nonlinear functional ϕ-Laplacian impulsive equations, Nonlinear Anal. 67(2007)827-841.
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.
J. F. Xu, Z. L. Yang, Positive solutions for a fourth order -Laplacian boundary value problem, Nonlinear Anal. 74 (2011) 2612-2623.
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