Servicios Personalizados
Revista
Articulo
Indicadores
-
Citado por SciELO
-
Accesos
Links relacionados
Compartir
Proyecciones (Antofagasta)
versión impresa ISSN 0716-0917
Proyecciones (Antofagasta) v.20 n.1 Antofagasta mayo 2001
http://dx.doi.org/10.4067/S0716-09172001000100003
NONLINEAR ELLIPTIC PROBLEMS
WITH RESONANCE AT THE TWO
FIRST EIGENVALUE : A
VARIATIONAL APPROACH
M. MOUSSAOUI and M. MOUSSAOUI
University Mohamed I - Oujda, Morocco
Abstract
We study the nonlinear elliptic problems with Dirichlet boundary condition
| -Dpu | | ¦(x, u) in W | |
u | | 0 on ¶W |
Resonance conditions at the first or at the second eigenvalue will be considered.
KEY WORDS: p-laplacian, eigenvalue, resonance, variational method.
References
[1] R.A. Adams, Sobolev spaces. Academic Press, New York, (1975). [ Links ]
[2] A. Anane Simplicité et isolation de la première valeur propre du p-laplacien avec poids. C.R. Ac. Sc. Paris, 305, pp. 725-728, (1987).
[3] A. Anane, J.P. Gossez Strongly nonlinear elliptic problems near resonance: A variational approach. Comm. Part. Diff. Eq. 15(8), pp. 1141-1159, (1990). [ Links ]
[4] A. Anane, N. Tsouli On the second eigenvalue of the p-laplacian, Nonlinear Partial Differential Equations, Pitman Research Notes 343, pp. 1-9, (1996). [ Links ]
[5] Bartolo P., Benci and Fortunato D. Abstrat critical point theorems and applications to some nonlinear problems with strong resonance at infinity, Nonlinear Analysis 7, pp. 981-1012, (1983).
[6] D.G. Costa, A.S. Oliveira Existence of solution for a class of semilinear elliptic problems at double resonance. Bol. Soc. BRAS. Mat., vol 19, pp. 21-37, (1988). [ Links ]
[7] D.G. Costa, C.A. MagalhVes Variational elliptic problems which are nonquadratic at infinity. Nonlinear Analysis, vol 23. Nº 11, pp. 1401-1412, (1994). [ Links ]
[8] M. Cuesta, D. de Figueiredo, J.P. Gossez The begining of the Fucik spectrum for the p-laplacian. J. Diff. Equat., 159, pp. 212-238, (1999). [ Links ]
[9] D.G. de Figueiredo, J.P. Gossez, Conditions de non résonance pour certains problèmes elliptiques semi-linéaire, C.R. Acad. Sci. Paris 302, pp. 543-545, (1986). [ Links ]
[10] D.G. de Figueireido, J.P. Gossez, Nonresonance below the first eigenvalue for a semilinear elliptic problems. Math. An. 281, pp. 589-610 (1988).
[11] D.G. de Figueiredo, J.P. Gossez, Strict monotonicity of eigenvalues and unique contination. Comm. Part. Diff. Eq., 17, pp. 339-346 (1992). [ Links ]
[12] A.R. El Amrouss, M. Moussaoui Non resonance entre les deux permières valeurs propres d'un problème quasi-lineaire. Bul. Bel. Math. Soc. 4, (1997). [ Links ]
[13] J. Mawhin, J.R. Ward, M. Willem, Variational methods of semilinear elliptic equations. Arch. Rat. Mech. An 95, pp. 269-277, (1986). [ Links ]
[14] João. Marcos. B. do Ó. Solution to perturbed eigenvalue problems of the p-laplacian in N*. J.D.E. N 11, pp. 1-15 (1997). [ Links ]
[15] M. Moussaoui, J.P. Gossez, A note on noresonance between consecutive eigenvalues for a semilinear elliptic problem Pitman Res. Notes in Math., 343, pp. 155-166, (196). [ Links ]
[16] P.H. Rabinowitz, Some minimax theorems and applications to nonlinear partial diffirential equations, Nonlinear Analysis, Cesari, Kannan and Weinberger. Eds, 161-177, Academic Press, Orlando, Fl. (1978).
[17] P.H. Rabinowitz, Some minimax methods in critical point theory with application to differential equations, CBMS, Regional conf. Ser. Math., vol 65 AMS, Providence Ri. (1986).
[18] M Schechter, Nonlinear elliptic boundary value problems at strong resonance, Amer. J. Math., 112, pp. 439-460, (1990). [ Links ]
[19] E.A. B. Silva, Linking theorems and applications to semilinear elliptic problems at resonance, Nonlinear Analysis TMA, 16, pp. 455-477, (1991). [ Links ]
Received: July, 2000.
M. Moussaoui and M. Moussaoui
Department of Mathematics
Faculty of Sciences
University Mohamed I
P.O. Box 524
60000 Oujda
Morocco
E-mail: moussaoui@sciences.univ-oujda.ac.ma