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Existence results for \(\phi\)-Laplacian impulsive differential equations with periodic conditions. (English) Zbl 1486.34071


MSC:

34B37 Boundary value problems with impulses for ordinary differential equations
34C25 Periodic solutions to ordinary differential equations
35R12 Impulsive partial differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations

References:

[1] Z, Pulse mass measles vaccination across age cohorts, Proc. Nat. Acad. Sci. USA, 90, 11698-11702 (1993)
[2] D. D. Bainov, P. S. Simeonov, <i>Systems with Impulse Effect: Stability, Theory and Applications</i>, New York: Halsted Press, 1989. · Zbl 0683.34032
[3] M. Benchohra, J. Henderson, S. K. Ntouyas, <i>Impulsive Differential Equations and Inclusions</i>, New York: Hindawi Publishing Corporation, 2006. · Zbl 1130.34003
[4] A, Multiple positive solutions for \(\phi \)-Laplacian BVPs, Panamer. Math. J., 17, 53-73 (2007) · Zbl 1133.34016
[5] C, Non-homogeneous boundary value problems for some nonlinear equations with singular \(\phi \)-Laplacian, J. Math. Anal. Appl., 352, 218-233 (2009) · Zbl 1170.34014
[6] C, Periodic solutions of nonlinear perturbations of \(\phi \)-Laplacians with possibly bounded \(\phi \), Nonlinear Anal. Theor., 68, 1668-1681 (2008) · Zbl 1147.34032
[7] A, Continuation theorems for periodic perturbations of autonomous systems, Trans. Amer. Math. Soc., 329, 41-72 (1992) · Zbl 0748.34025
[8] S. Djebali, L. Gorniewicz, A. Ouahab, <i>Existence and Structure of Solution Sets for Impulsive</i> <i>Differential Inclusions</i>, Lecture Notes, Nicolaus Copernicus University, 13 (2012). · Zbl 1250.34002
[9] S. Djebali, L. Gorniewicz, A. Ouahab, <i>Solutions Sets for Differential Equations and Inclusions</i>, Berlin: Walter de Gruyter, 2013. · Zbl 1258.34002
[10] P. Fitzpatrick, M. Martelli, J. Mawhin, et al. <i>Topological Methods for Ordinary Differential</i> <i>Equations</i>, Springer-Verlag, 1991.
[11] R. E. Gaines, J. Mawhin, <i>Coincidence Degree and Nonlinear Differential Equations</i>, Berlin: Springer-Verlag, 1977. · Zbl 0339.47031
[12] W, An extension of Mawhin’s continuation theorem and its application to boundary value problems with a <i>p</i>-Laplacian, Nonlinear Anal. Theor., 58, 477-488 (2004) · Zbl 1074.34014
[13] J. R. Graef, J. Henderson, A. Ouahab, <i>Impulsive Differential Inclusions: A Fixed Pont Approach, </i> Berlin: Walter de Gruyter, 2013. · Zbl 1285.34002
[14] A. Halanay, D. Wexler, <i>Teoria Calitativa a Systeme cu Impulduri</i>, Editura Republicii Socialiste Romania, Bucharest, 1968. · Zbl 0176.05202
[15] J, Existence and topological structure of solution sets for \(\phi \)-Laplacian impulsive differential equations, Electron. J. Differ. Eq., 56, 1-16 (2012) · Zbl 1244.34015
[16] V. Lakshmikantham, D. Bainov, P.S. Simenov, <i>Theory of Impulsive Differential Equations</i>, Singapore: World Scientific, 1989. · Zbl 0719.34002
[17] J, Periodic solutions of nonlinear functional differential equations, J. Differ. Eq., 10, 240-261 (1971) · Zbl 0223.34055
[18] R, Periodic solutions for nonlinear systems with p-Laplacian-like operators, J. Differ. Eq., 145, 367-393 (1998) · Zbl 0910.34051
[19] V. D. Milman, A. A. Myshkis, <i>On the stability of motion in the presence of impulses (in Russian), </i> Sib. Math. J., 1 (1960), 233-237. · Zbl 1358.34022
[20] J, Variational approach to impulsive differential equations, Nonlinear Anal. Real., 10, 680-690 (2009) · Zbl 1167.34318
[21] D, Topological Degree Theory and Applications, Chapman and Hall (2006) · Zbl 1095.47001
[22] L, Existence of periodic solutions for second order delay differential equations with impulses, Electron. J. Differ. Eq., 37, 1-12 (2011) · Zbl 1216.34078
[23] D, Periodic solutions for ordinary differential equations with sublinear impulsive effects, J. Math. Anal. Appl., 303, 288-303 (2005) · Zbl 1071.34005
[24] I, Dirichlet problem with \(\phi \)-Laplacian and mixed singularities, Nonlinear Oscil., 11, 80-96 (2008) · Zbl 1282.34029
[25] I, Second order periodic problem with \(\phi \)-Laplacian and impulses, Nonlinear Anal. Theor., 63, 257-266 (2005) · Zbl 1159.34319
[26] I, Periodic problems with \(\phi \)-Laplacian involving non-ordered lower and upper functions, Fixed Point Theory, 6, 99-112 (2005) · Zbl 1069.34025
[27] I, Existence result for impulsive second order periodic problems, Nonlinear Anal. Theor., 59, 133-146 (2004) · Zbl 1084.34031
[28] M. Samoilenko, N. Perestyuk, <i>Impulsive Differential Equations</i>, Singapore: World Scientific, 1995. · Zbl 0837.34003
[29] N. A. Perestyuk, V. A. Plotnikov, A. M. Samoilenko, et al. <i>Differential Equations with Impulse</i> <i>Effects. Multivalued Right-hand Sides with Discontinuities, </i> Berlin: Walter de Gruyter, 2011. · Zbl 1234.34002
[30] J, Existence and multiplicity of solutions for impulsive differential equation with two parameters via variational method, Nonlinear Anal. Theor., 73, 440-449 (2010) · Zbl 1198.34037
[31] J, Dirichlet boundary value problem for differential equation with \(\phi \)-Laplacian and state-dependent impulses, Math. Slovaca, 67, 483-500 (2017) · Zbl 1413.34121
[32] J, The existence of periodic solutions of the n-species Lotka-Volterra competition systems with impulsive, Chaos, Solitons, Fractals, 22, 181-188 (2004) · Zbl 1058.92046
[33] Z, Existence of solutions for second order impulsive differential equations, Appl. Math. JCU, 12, 307-320 (1997) · Zbl 0885.34018
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