Multiplicity results for periodic solutions of a second order quasilinear ode with asymmetric nonlinearities

Nonlinear Analysis, Theory, Methods and Applications

Volumn 33, Issue 2, 1998, Pages 139-160

  Liu, Bin ^a  

^a PEKING UNIVERSITY   (China)

Author keywords

Asymmetric nonlinearities; One dimensional p Laplace operator; Periodic solutions; Subharmonic solutions

Indexed keywords

BOUNDARY CONDITIONS; EIGENVALUES AND EIGENFUNCTIONS; FUNCTIONS; MATHEMATICAL OPERATORS; THEOREM PROVING;

DIRICHLET BOUNDARY CONDITIONS; LAPLACE OPERATORS; NONLINEAR OPERATORS; POINCARE-BIRKHOFF FIXED THEOREM;

DIFFERENTIAL EQUATIONS;

EID: 0032117230     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0362-546x(97)00522-1     Document Type: Article

References (10)

1. Ambrosetti, A. and Prodi, G., On the inversion of some differentiable mappings with singularities between Banach spaces. Ann. Math. Pura Appl., 1972, 93, 231-247.
2. Berger, M. and Podolak, E., On the solutions of a nonlinear Dirichlet problem. Indiana Univ. Math. J., 1975, 24, 837-846.
3. Garcia-Huidobro, M., Manasevich, R. and Zanolin, F., Stongly nonlinear second ODE's with rapidly growing terms, J. Math. Anal. Appl. (To appear.)
4. Boccardo, L., Drábek, P., Giachetti, D. and Kucera, M., Generalization of Fredholm alternative for nonlinear differential operators. Nonlinear Analysis, 1986, 10, 1083-1103.
5. p-2u′)′ + f(t, u) = 0, u(0) = u(T) = 0, p > 1. J. Differential Equations, 1989, 80, 1-13.
6. Del Pino, M., Manasevich, R. and Murua, A., Existence and multiplicity of solutions with prescribed period for a second order quasilinear o.d.e. Nonlinear Analysis, 1992, 18, 79-92.
7. Fabry, C. and Fayyad, D., Periodic solutions of second order differential equations with a p-Laplacian and asymmetric nonlinearities. Rend. Ist. Mat. Univ. Trieste, 1992, 24, 207-227.
8. Rebelo, C. and Zanolin, F., Multiplicity results for periodic solutions of second order ODEs with asymmetric nonlinearities. Trans. Amer. Math. Soc. (To appear.)
9. El Hachimi, A. and De Thelin, F., Infinitely many radially symmetric solutions for a quasilinear elliptic problem in a ball. Preprint.
10. Ding, W. Y., A generalization of the Poincaré-Birkhoff theorem. Proc. Amer. Math. Soc., 1983, 88, 341-346.