Neumann and periodic boundary-value problem for quasilinear ordinary differential equation with a nonlinearity in the derivative

Electronic Journal of Differential Equations

Volumn 2000, Issue , 2000, Pages

  Gir, Petr ^a  

^a UNIVERSITY OF WEST BOHEMIA   (Czech Republic)

Author keywords

Landesmann Lazer condition; Leray Schauder degree; p Laplacian

Indexed keywords

EID: 52849111689     PISSN: 10726691     EISSN: 10726691     Source Type: Journal    
DOI: None     Document Type: Article

References (18)

1. Ambrosetti, A., and Prodi, G., A Primer of Nonlinear Analysis, Cambridge University Press, Cambridge, 1993.
2. Arcoya, D., and Orsina, L., Landesman-Lazer conditions and quasilinear elliptic equations, Nonlinear Anal., 28 (1997), 1623-1632.
3. Boccardo, L., Drâbek, P., and Kucera, M., Landasman-Lazer conditions for strongly nonlinear boundary-value problems, Comment. Math. Univ. Carolin., 30 (1989), 411-427.
4. Canada, A., and Drâbek, P., On semilinear problems with nonlinearities depending only on derivatives, SIAM J. Math. Anal., 27 (1996), 543-557.
5. Coddington E. A., Levinson, N., Theory of ordinary differential equations, McGraw-Hill, New York, 1955.
6. Dancer, E. N., On the ranges of certain damped nonlinear differential equation, Ann. Mat. Pura Appl., 119 (1979), 281-295.
7. del Pino, M., Acerca de un problema cuasilineal de secundo orden, Diploma Thesis, Universidad de Chile, Santiago de Chile, 1987.
8. Fucik, S., Solvability of Nonlinear Equation and Boundary Value Problems, D. Reidel Publishing Company, Dordrecht, 1980.
9. Garcia-Huidobro, M., Manâsevich, R., and Zanolin, F., A Fredholm-like Result for Strongly Nonlinear Second Order ODE's, J. Differential Equations, 114 (1994), 132-167.
10. Garcia-Huidobro, M., Manâsevich, R., and Zanolin, F., Strongly Nonlinear Second Order ODE's with Unilateral Conditions, Differential and Integral Equations, 6 (1993), 1057-1078.
11. Kannan, R., and Seikkala, S., Existence of solutions to a periodic boundary-value problem, in 'Function Spaces, Differential Operators and Nonlinear Analysis ' (Vesa Mustonen, Jiff Rakosnik, editors), Mathematical Institute AS CR, Prague, 1999, 149-156.
12. Kotek, Z., Kubik, S., Nonlinear circuits (in Czech), SNTL, Prague, 1962.
13. Landesman, E. M., and Lazer, A. C., Nonlinear perturbations of linear elliptic boundary-value problems at resonance, J. Math. Mech., 19 (1970), 609-623.
14. Manâsevich, R., and Mawhin, J., Periodic solutions for nonlinear systems with p-Laplacian-like operators, J. Differential Equations, 145 (1998), 367393.
15. Mawhin, J., Willem, M., Critical point theory and Hamiltonian systems, Springer Verlag, 1989.
16. Mawhin, J., Some remarks on semilinear problems at resonance where the nonlinearity depends only on the derivatives, Acta Math. Inform. Univ. Ostraviensis, 2 (1994), 61-69.
17. Ames, W. F., Nonlinear partial differential equations in engineering, Academic press, New York, 1965.
18. Zeidler, E., Nonlinear Functional Analysis and its Applications I, Springer-Verlag, Berlin, 1986.