Nonresonance between two eigenvalues not necessarily consecutive
DOI:
https://doi.org/10.4067/S0716-09172005000200001Keywords:
Variational elliptic problems, Resonance.Abstract
Abstract
In this paper we study the existence of solutions for a semilinear elliptic problem in case two eigenvalues are not necessarily consecutive.
Résumé
Dans cet article, nous étudions l’existence des solutions entre deux valeurs propres non nécessairement consecutives d’un problème semi-linéaire elliptique.
References
[1] S. Ahmad, A. C. Lazer, & J. L. Paul, Elementary critical point theory and perturbations of elliptic boundary value problems at resonance, Indiana Univ.math. J. 25, pp. 933-944, (1976).
[2] H. Amman, & G. Mancini, Some applications of monotone operator theory to resonance problems, Nonlinear Analysis T. M. A. 3, pp. 815-830, (1979).
[3] P. Bartolo, V. Benci & D. Fortunato, Abstract critical point theorems and applications to some nonlinear problems with strong resonance at infinity, Nonlinear Analysis 7, pp. 981-1012, (1983).
[4] H. Berestycki & D. G. De Figueiredo, Double resonance in semilinear elliptic problems, Communs partial diff. Eqns 6, pp. 91-120, (1981).
[5] G. Cerami, Un criterio de esistenza per i punti critici su varietá ilimitate, Rc. Ist. Lomb. Sci. Lett. 121, pp. 332-336, (1978).
[6] D. G. Costa & A. S. Oliveira, Existence of solution for a class of semilinear elliptic problems at double resonance, Bol. Soc. Bras. Mat. 19 , pp. 21-37, (1988).
[7] D. G. De Figueiredo & J. P. Gossez, Conditions de non résonance pour certains problémes elliptiques semi-lin´eaires, C. R. Acad. Sc. Paris, 302, pp. 543-545, (1986).
[8] C. L. Dolph, Nonlinear integral equations of the Hammertein type, Trans. Amer. Math. SOC., 66, pp. 289-307, (1949).
[9] D. Del Santo et P. Omari, Nonresonance conditions on the potentiel for a semilinear elleptic problem, J. Differential Equations, 108, pp. 120-138, (1994).
[10] A. R. El Amrouss & M. Moussaoui, Resonance at two consecutive eigenvalues for semilinear elliptic problem: A variational approach, Ann. Sci. Math. Qubec 23, no. 2, pp. 157-171, (1999).
[11] J. P. Gossez & M. Moussaoui, A note on resonance between consecutive eigenvalues for a semilinear elliptic problem, Pitman Res. Notes in Math., 343, pp. 155-166, (1996).
[12] E. M. Landesman & A. C. Lazer, Nonlinear perturbations of linear elliptic boundary value problems at resonance, J. Math. Mech. 19, pp. 609-623, (1970).
[13] J. Mawhin, & J. R.Ward, Nonresonance and existence for nonlinear elliptic boundary value problems, Nonlinear Analysis T. M. A., pp. 677-684, (1981).
[14] P. Omari & F. Zanolin, Resonance at two consecutive eigenvalues for semilinear elliptic equations, Annali di matematica pura ed applicata, pp. 181-198, (1993).
[2] H. Amman, & G. Mancini, Some applications of monotone operator theory to resonance problems, Nonlinear Analysis T. M. A. 3, pp. 815-830, (1979).
[3] P. Bartolo, V. Benci & D. Fortunato, Abstract critical point theorems and applications to some nonlinear problems with strong resonance at infinity, Nonlinear Analysis 7, pp. 981-1012, (1983).
[4] H. Berestycki & D. G. De Figueiredo, Double resonance in semilinear elliptic problems, Communs partial diff. Eqns 6, pp. 91-120, (1981).
[5] G. Cerami, Un criterio de esistenza per i punti critici su varietá ilimitate, Rc. Ist. Lomb. Sci. Lett. 121, pp. 332-336, (1978).
[6] D. G. Costa & A. S. Oliveira, Existence of solution for a class of semilinear elliptic problems at double resonance, Bol. Soc. Bras. Mat. 19 , pp. 21-37, (1988).
[7] D. G. De Figueiredo & J. P. Gossez, Conditions de non résonance pour certains problémes elliptiques semi-lin´eaires, C. R. Acad. Sc. Paris, 302, pp. 543-545, (1986).
[8] C. L. Dolph, Nonlinear integral equations of the Hammertein type, Trans. Amer. Math. SOC., 66, pp. 289-307, (1949).
[9] D. Del Santo et P. Omari, Nonresonance conditions on the potentiel for a semilinear elleptic problem, J. Differential Equations, 108, pp. 120-138, (1994).
[10] A. R. El Amrouss & M. Moussaoui, Resonance at two consecutive eigenvalues for semilinear elliptic problem: A variational approach, Ann. Sci. Math. Qubec 23, no. 2, pp. 157-171, (1999).
[11] J. P. Gossez & M. Moussaoui, A note on resonance between consecutive eigenvalues for a semilinear elliptic problem, Pitman Res. Notes in Math., 343, pp. 155-166, (1996).
[12] E. M. Landesman & A. C. Lazer, Nonlinear perturbations of linear elliptic boundary value problems at resonance, J. Math. Mech. 19, pp. 609-623, (1970).
[13] J. Mawhin, & J. R.Ward, Nonresonance and existence for nonlinear elliptic boundary value problems, Nonlinear Analysis T. M. A., pp. 677-684, (1981).
[14] P. Omari & F. Zanolin, Resonance at two consecutive eigenvalues for semilinear elliptic equations, Annali di matematica pura ed applicata, pp. 181-198, (1993).
Published
2017-04-20
How to Cite
[1]
A. R. El Amrouss, “Nonresonance between two eigenvalues not necessarily consecutive”, Proyecciones (Antofagasta, On line), vol. 24, no. 2, pp. 89-104, Apr. 2017.
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