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Autovalori di un problema ellittico dipendente da un parametro in modo non lineare. (Italian) Zbl 0485.35038

MSC:

35J25 Boundary value problems for second-order elliptic equations
35P15 Estimates of eigenvalues in context of PDEs
35B50 Maximum principles in context of PDEs
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References:

[1] C. Del Pace - G. PAPI FROSALI, Principio di massimo ed antofunzioni positive per una famiglia di operatori ellittici quadratica nel parametro, Analisi Funzionale e Applicazioni , suppl. B.U.M.I. , 1 ( 1980 ), pp. 219 - 237 . MR 677699 | Zbl 0449.35022 · Zbl 0449.35022
[2] A. Devinatz - R. ELLIS - A. FRIEDMAN, The asymptotic behavior of the first real eigenvalue of second order elliptic operators with a small parameter in the highest derivatives II , Indiana Univ. Math. J. , 23 ( 1974 ), pp. 991 - 1011 . MR 344709 | Zbl 0263.35026 · Zbl 0263.35026 · doi:10.1512/iumj.1974.23.23081
[3] J. Eisenfeld , On simmetrization and roots of quadratic eigenvalue problems , J. Functional Analysis , 9 ( 1972 ), pp. 410 - 422 . MR 296727 | Zbl 0231.47015 · Zbl 0231.47015 · doi:10.1016/0022-1236(72)90018-3
[4] I.C. Gohberg - M. G. KREIN, Introduction to the theory of linear nonselfadjoint operators , American Mathematical Society , Providence R.I. , 1969 . MR 246142 | Zbl 0181.13504 · Zbl 0181.13503
[5] T. Kato , Perturbation theory for linear operators , Springer-Verlag , New York , 1966 . MR 203473 | Zbl 0148.12601 · Zbl 0148.12601
[6] M.A. Krasnosel’skii , Positive solutions of operator equations , Nordhoff , Groningen , 1966 . MR 181881
[7] M.G. Krein - H. LANGER, A contribution to the theory of quadratic pencils of selfadjoint operators , Soviet. Math. Dokl. , 5 - 1 ( 1964 ), pp. 266 - 268 . Zbl 0198.47102 · Zbl 0198.47102
[8] C. Miranda , Partial differential equations of elliptic type , Springer-Verlag , New York , 1970 . MR 284700 | Zbl 0198.14101 · Zbl 0198.14101
[9] M. Protter - H. WEINBERGER, On the spectrum of general second order operators , Bull. Amer. Math. Soc. , 72 ( 1966 ), pp. 251 - 255 . Article | MR 190527 | Zbl 0141.09901 · Zbl 0141.09901 · doi:10.1090/S0002-9904-1966-11485-4
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