Second-order periodic problem with φ-Laplacian and impulses

Nonlinear Analysis, Theory, Methods and Applications

Volumn 63, Issue 5-7, 2005, Pages

  Rachůnková, Irena ^a   Tvrdý, Milan ^b  

^a PALACKÝ UNIVERSITY   (Czech Republic)

^b MATHEMATICAL INSTITUTE   (Czech Republic)

Author keywords

Laplacian; Impulses; Lower upper functions; Periodic solutions

Indexed keywords

FUNCTIONS; LAPLACE TRANSFORMS; NUMERICAL METHODS;

IMPULSES; LOWER/UPPER FUNCTIONS; PERIODIC FUNCTIONS;

PROBLEM SOLVING;

EID: 28044440527     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2004.09.017     Document Type: Conference Paper

References (19)

1. A. Cabada, P. Habets, R. Pouso, Lower and upper solutions for the periodic problem associated with a φ -Laplacian equation, EQUADIFF 1999 - International Conference on Differential Equations, vols. 1, 2, Berlin, 1999, World Sci. Publishing, River Edge, NJ, 2000, pp. 491-493.
2. A. Cabada, and R. Pouso Existence result for the problem (φ (u ′ ) ) ′ = f (t, u, u ′ ) with periodic and Neumann boundary conditions Nonlinear Anal. Theory Methods Appl. 30 1997 1733 1742
3. M. Cherpion, C. De Coster, and P. Habets Monotone iterative methods for boundary value problems Differential Integral. Equations 12 3 1999 309 338
4. M. Del Pino, R. Manásevich, and A. Murúa Existence and multiplicity of solutions with prescribed period for a second order quasilinear O.D.E Nonlinear Anal. Theory Methods Appl. 18 1992 79 92
5. C. Fabry, and D. Fayyad Periodic solutions of second order differential equation with a p-Laplacian and asymmetric nonlinearities Rend. Ist. Mat. Univ. Trieste 24 1992 207 227
6. P. Girg, Neumann and periodic boundary-value problems for quasilinear ordinary differential equations with a nonlinearity in the derivative, Electron. J. Differential Equations 2000, Paper No.63, 28pp, electronic only, 2000.
7. P. Jebelean, and J. Mawhin Periodic solutions of singular nonlinear perturbations of the ordinary p-Laplacian Adv. Nonlinear Stud. 2 2002 299 312
8. Liu Bin Multiplicity results for periodic solutions of a second order quasilinear ordinary differential equations with asymmetric nonlinearities Nonlinear Anal. Theory Methods Appl. 33 2 1998 139 160
9. Liu Bing Periodic solutions of dissipative dynamical systems with singular potential and p-Laplacian Ann. Polon. Math. 79 2 2002 109 120
10. R. Manásevich, and J. Mawhin Periodic solutions for nonlinear systems with p-Laplacian like operators J. Differential Equations 145 1998 367 393
11. J. Mawhin Some boundary value problems for Hartman-type perturbations of the ordinary vector p-Laplacian Nonlinear Anal. Theory Methods Appl. 40 2000 497 503
12. J. Mawhin, and A. Ure na A Hartman-Nagumo inequality for the vector ordinary p-Laplacian and application to nonlinear boundary value problem J. Inequal. Appl. 7 5 2002 701 725
13. I. Rachůnková, and M. Tvrdý Nonmonotone impulse effects in second order periodic boundary value problems Abstract Anal. Appl. 2004 7 2004 577 590
14. I. Rachůnková, M. Tvrdý, Second order periodic problem with φ -Laplacian and impulses - Part I, Preprint 155, Mathematical Institute of the Academy of Science of the Czech Republic, 2004 [available as http://www.math.cas.cz/~tvrdy/lapl1.pdf or http://www.math.cas.cz/~tvrdy/ lapl1.ps ].
15. I. Rachůnková, M. Tvrdý, Second order periodic problem with φ -Laplacian and impulses - Part II, Preprint 156, Mathematical Institute of the Academy of Sciences of the Czech Republic, 2004 [available as http://www.math.cas.cz/~tvrdy/lapl2.pdf or http://www.math.cas.cz/~tvrdy/ lapl2.ps ].
16. I. Rachůnková, M. Tvrdý, Existence results for impulsive second order periodic problems, Nonlinear Anal. Theory Methods Appl. 59 (2004) 133-146.
17. S. Staněk Periodic boundary value problem for second order functional differential equations Math. Notes Miskolc 1 2000 63 81
18. S. Staněk On solvability of singular periodic boundary value problems Nonlinear Oscil. 4 2001 529 538
19. Yan Ping Nonresonance for one-dimensional p-Laplacian with regular restoring J. Math. Anal. Appl. 285 2003 141 154