On the existence of periodic solutions for p-Laplacian generalized Liénard equation

Nonlinear Analysis, Theory, Methods and Applications

Volumn 60, Issue 1, 2005, Pages 65-75

  Cheung, Wing Sum ^a   Ren, Jingli ^b  

^a UNIVERSITY OF HONG KONG   (Hong Kong)

^b INSTITUTE OF SYSTEMS SCIENCE   (China)

Author keywords

Deviating argument; Mawhin's continuation theorem; Periodic solution

Indexed keywords

CONFORMAL MAPPING; FUNCTIONS; INTEGRAL EQUATIONS; MATHEMATICAL OPERATORS; NONLINEAR EQUATIONS; PROBLEM SOLVING; THEOREM PROVING;

DEVIATING ARGUMENT; MAWHIN'S CONTINUATION THEOREM; PERIODIC FUNCTIONS; PERIODIC SOLUTIONS;

LAPLACE TRANSFORMS;

EID: 9344243570     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2004.08.021     Document Type: Article

References (10)

1. M.A. Del Pino, R.F. Manásevich, Multiple solutions for the p-Laplacian under global non-resonance, Proc. Amer. Math. Soc. 112 (1991) 131-138.
2. M.A. Del Pino, R.F. Manásevich, A. Murua, Existence and multiple of solutions with prescribed period for a second order quasi-linear ordinary differential equation, Nonlinear Anal. TMA 18 (1992) 79-92.
3. C. Fabry, D. Fayyad, Periodic solutions of second order differential equations with a p-Laplacian and asymmetric nonlinearities, Rend. Ist. Univ. Trieste. 24 (1992) 207-227.
4. R.E. Gaines, J.L. Mawhin, Coincidence Degree and Nonlinear Differential Equations, Springer, Berlin, 1977.
5. X. Huang, Z. Xiang, On the existence of 2π-periodic solutions of Duffing type equation x″(t) + g(x(t -t) = p(t), Chinese Sci. Bull: 39 (1994) 201-203 (in Chinese).
6. B. Liu, Multiplicity results for periodic solutions of a second order quasi-linear ODE with asymmetric nonlinearities, Nonlinear Anal. TMA 33 (1998) 139-160.
7. S. Lu, W. Ge, Periodic solutions for a kind of second order differential equations with multiple deviating arguments, Appl. Math. Comput. 146 (2003) 195-209.
8. S. Ma, Z. Wang, J. Yu, An abstract theorem at resonance and its applications, J. Differ. Equations 145 (1998) 274-294.
9. S. Ma, Z. Wang, J. Yu, Coincidence degree and periodic solutions of Duffing equations, Nonlinear Analysis TMA 34 (1998) 443-460.
10. R.F. Manásevich, J. Mawhin, Periodic solutions for nonlinear systems with p-Laplacian like operarors, J. Differ. Equations 145 (1998) 367-393.