Spectre d’ordre un pour un probleme hyperbolique et applications
DOI:
https://doi.org/10.4067/S0716-09172002000200001Keywords:
D’Alembertian operator, Fredholm alternative, nonlinear problem, spectra, operador de D'Alembert, alternativa de Fredholm, problema no lineal, espectros.Abstract
We define and determine the spectrum of order one of the d’Alembertian operator. We resolve the Fredholm alternative and the nonlinear problem at resonance.Downloads
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References
[1] A. Anane-O. Chakrone-J. P. Gossez, Spectre d’ordre supérieure et probleme de non résonance, C. R. Acad. Sci.Paris, t325, serie I, pp. 33-36, (1997).
[2] A. Anane-O. Chakrone-J. P. Gossez, Spectre d’ordre supérieure et probleme aux limites quasi-linéaires, Bolletino U.M.I. (8) 4-B, pp. 483-519, (2001).
[3] A. K Bennaoum,on the Dirichlet problem for the nonlinear wave equation in bounded domains with corner points, institut de mathématique pure et appliquée université catholique de Louvain-Belgique, recherches de mathematique 51 (1996).
[4] A. K. Bennaoum-J. Mawhin, periodic solutions of some semilinear wave equations on balls and on spheres, institut de Mathématique pure et appliquée université catholique de Louvain-Belgique, recherches de mathématique 15, (1992).
[5] J. Berkovits-V. Mustonen, On the resonance for semilinear equations with normal linear part, J. Math. Maroc 2, pp. 115-123, (1994).
[6] J. Berkovits-V. Mustonen, An extension of Leray-Schauder degree and applications to nonlinear wave equations, Differential and Integral Equations 3, pp. 945-963, (1990).
[7] J. Berkovits-V. Mustonen, On semilinear wave equations at resonance. proceedings of the first world congress of nonlinear analysts, 1992. Editor: V. Lakshmikantham, Berlin, New York, (1996).
[8] J. Berkovits-V. Mustonen,an application of topologique degree to semilinear equations with nonlinearities strongly monotones, Bull. London Math. Soc. 23, pp. 470-476, (1991).
[9] J. Berkovits-V. Mustonen, On multiple solutions for a class of semilinear wave equations, Nonlinear Analysis: theory and applications, Vol. 16, No. 5, pp. 421-434, (1991).
[10] J. Berkovits-V. Mustonen: On nonresonance for systems of semilinear wave equations, Nonlinear Analysis: theory and applications, Vol. 29, pp. 627-638, (1997)
[11] H. Brézis, Analyse fonctionnelle, théorie et applications, Masson (1987).
[12] H. Brézis-L. Nirenberg, Characterization of the ranges of some nonlinear operators and applications to boundary value problems, Ann. Scuola Norm. Sup. Pisa (4) 5, pp. 225-326, (1978).
[13] O. Chakrone, these de doctorat.université d’oujda (1998).
[14] R. Dautray-J. L. Lions, Analyse mathématique et calcul numérique pour les sciences et les techniques, T2 Masson (1985).
[15] E. Landesman, A. Lazer, Nonlinear perturbation of linear elliptic boundary value problems at resonance, J. Math. Mech. 19, pp. 609-623, (1970).
[2] A. Anane-O. Chakrone-J. P. Gossez, Spectre d’ordre supérieure et probleme aux limites quasi-linéaires, Bolletino U.M.I. (8) 4-B, pp. 483-519, (2001).
[3] A. K Bennaoum,on the Dirichlet problem for the nonlinear wave equation in bounded domains with corner points, institut de mathématique pure et appliquée université catholique de Louvain-Belgique, recherches de mathematique 51 (1996).
[4] A. K. Bennaoum-J. Mawhin, periodic solutions of some semilinear wave equations on balls and on spheres, institut de Mathématique pure et appliquée université catholique de Louvain-Belgique, recherches de mathématique 15, (1992).
[5] J. Berkovits-V. Mustonen, On the resonance for semilinear equations with normal linear part, J. Math. Maroc 2, pp. 115-123, (1994).
[6] J. Berkovits-V. Mustonen, An extension of Leray-Schauder degree and applications to nonlinear wave equations, Differential and Integral Equations 3, pp. 945-963, (1990).
[7] J. Berkovits-V. Mustonen, On semilinear wave equations at resonance. proceedings of the first world congress of nonlinear analysts, 1992. Editor: V. Lakshmikantham, Berlin, New York, (1996).
[8] J. Berkovits-V. Mustonen,an application of topologique degree to semilinear equations with nonlinearities strongly monotones, Bull. London Math. Soc. 23, pp. 470-476, (1991).
[9] J. Berkovits-V. Mustonen, On multiple solutions for a class of semilinear wave equations, Nonlinear Analysis: theory and applications, Vol. 16, No. 5, pp. 421-434, (1991).
[10] J. Berkovits-V. Mustonen: On nonresonance for systems of semilinear wave equations, Nonlinear Analysis: theory and applications, Vol. 29, pp. 627-638, (1997)
[11] H. Brézis, Analyse fonctionnelle, théorie et applications, Masson (1987).
[12] H. Brézis-L. Nirenberg, Characterization of the ranges of some nonlinear operators and applications to boundary value problems, Ann. Scuola Norm. Sup. Pisa (4) 5, pp. 225-326, (1978).
[13] O. Chakrone, these de doctorat.université d’oujda (1998).
[14] R. Dautray-J. L. Lions, Analyse mathématique et calcul numérique pour les sciences et les techniques, T2 Masson (1985).
[15] E. Landesman, A. Lazer, Nonlinear perturbation of linear elliptic boundary value problems at resonance, J. Math. Mech. 19, pp. 609-623, (1970).
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2017-05-22
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How to Cite
[1]
“Spectre d’ordre un pour un probleme hyperbolique et applications”, Proyecciones (Antofagasta, On line), vol. 21, no. 2, pp. 109–125, May 2017, doi: 10.4067/S0716-09172002000200001.
