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Sur un problème aux valeurs propres non linéaire. (French) Zbl 0444.35065


MSC:

35P30 Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs
65H10 Numerical computation of solutions to systems of equations
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References:

[1] S. Agmon,Lectures on Elliptic Boundary Value Problem, Math. Studies No. 2, Van Nostrand, 1965. · Zbl 0142.37401
[2] Baouendi, M. S.; Sjöstrand, J., Régularité analytique pour des opérateurs elliptiques singuliers en un point, Ark. Mat., 14, 9-33 (1976) · Zbl 0334.35021 · doi:10.1007/BF02385820
[3] Cordes, H. O., On compactness of commutators of multiplications and convolutions and boundness of pseudodifferential operators, J. Functional Analysis, 18, 115-131 (1975) · Zbl 0306.47024 · doi:10.1016/0022-1236(75)90020-8
[4] N. Dunford and J. T. Schwartz,Linear Operators, Vol. 2, Interscience Publ., 1963. · Zbl 0128.34803
[5] Friedman; Shinbrot, Non-linear eigenvalue problems, Acta Math., 121, 77-128 (1968) · Zbl 0162.45704 · doi:10.1007/BF02391910
[6] I. Gohberg and M. G. Krein,Introduction à la théorie des opérateurs linéaires non autoadjoints, Dunod, 1972.
[7] B. Helffer,Remarques sur des résultats de G. Métivier sur la non-hypo-analyticité, Séminaire de l’Université de Nantes, exposé n^o 9, 1978-79.
[8] Helffer, B.; Nourrigar, J., Hypoellipticité pour des groupes nilpotents de rang de Qtudies 3, Comm. Partial Differential Equations, 3, 643-743 (1978) · Zbl 0385.35015 · doi:10.1080/03605307808820075
[9] Keldysh, M. V., On the completness of the eigenfunctions o of classes of non-selfadjoint linear operators, Russian Math. Surveys, 26, No. 4, 15-44 (1971) · Zbl 0225.47008 · doi:10.1070/rm1971v026n04ABEH003985
[10] M. G. Krein and H. Langer,On some mathematical principles in the linear theory of damped oscillations of continua, inIntegral Equations and Operator Theory, Vol. 1-3 (1978), 364-399. · Zbl 0401.47017
[11] G. Metivier,Une classe d’opérateurs non hypoelliptiques analytiques, Séminaire Goulaouic-Schwartz, 1978-79. · Zbl 0419.35022
[12] Robert, D., Propriétés spectrales d’opérateurs pseudodifferentiels, Comm. Partial Differential Equations, 3, 755-826 (1978) · Zbl 0392.35056 · doi:10.1080/03605307808820077
[13] Titchmarsh, E. C., The Theory of Functions (1939), London: Oxford Univ. Press, London · JFM 65.0302.01
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