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Amann, Herbert; Ambrosetti, Antonio; Mancini, Giovanni

Elliptic equations with noninvertible Fredholm linear part and bounded nonlinearities. (English) Zbl 0368.35032

Math. Z. 158, 179-194 (1978).
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scan of Zbl 0368.35032

Cited in 2 Reviews
Cited in 61 Documents

MSC:

35J60 Nonlinear elliptic equations
47J05 Equations involving nonlinear operators (general)
35R20 Operator partial differential equations (= PDEs on finite-dimensional spaces for abstract space valued functions)
35J25 Boundary value problems for second-order elliptic equations
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Full Text: DOI EuDML

References:

[1] Agmon, S., Douglis, A., Nirenberg, L.: Estimates near the boundary of elliptic partial differential equations satisfying general boundary conditions. I. Commun. pure appl. Math.12, 623-727 (1959) · Zbl 0093.10401 · doi:10.1002/cpa.3160120405
[2] Amann, H.: Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces. SIAM Review18, 620-709 (1976) · Zbl 0345.47044 · doi:10.1137/1018114
[3] Amann, H.: Existence and multiplicity theorems for semi-linear elliptic boundary value problems. Math. Z.150, 281-295 (1976) · Zbl 0331.35026 · doi:10.1007/BF01221152
[4] Amann, H., Crandall, M.G.: On some existence theorems for semilinear elliptic equations. Ind. Uni. Math. J. To appear · Zbl 0391.35030
[5] Ambrosetti, A., Mancini, G.: Existence and multiplicity results for nonlinear elliptic problems with linear part at resonance. J. Diff. Equations, to appear · Zbl 0393.35032
[6] Ambrosetti, A., Mancini, G.: Theorems of existence and multiplicity for nonlinear elliptic problems with noninvertible linear part. Ann. Scuola norm. sup. Pisa, Sci. fis. mat., III. Ser. to appear
[7] Berger, M.S., Podolak, E.: On nonlinear Fredholm operator equations. Bull. Amer. math. Soc.80, 861-864 (1974) · Zbl 0299.47034 · doi:10.1090/S0002-9904-1974-13543-3
[8] Brezis, H., Nirenberg, L.: Characterizations of the ranges of some nonlinear operators and applications to boundary value problems. Ann. Scuola norm. sup. Pisa, Sci. fis. mat., III. Ser. to appear
[9] Cesari, L.: Functional Analysis, nonlinear differential equations, and the alternative method. In: Nonlinear Functional Analysis and Differential Equations (East Lansing 1975) L. Cesari, R. Kannan & J.D. Schuur Eds. pp. 1-197. New York-Basel: M. Dekker Inc. 1976
[10] Fu?ik, S.: Ranges of nonlinear operators. Lecture Notes. Prague: Charles University 1977
[11] Kazdan, J.L., Warner, F.W.: Remarks on some quasilinear elliptic equations. Commun. pure appl. Math.28, 567-597 (1975) · Zbl 0325.35038 · doi:10.1002/cpa.3160280502
[12] Landesman, E.A., Lazer, A.C.: Nonlinear perturbations of linear elliptic boundary value problems at resonance. J. Math. Mech.19, 609-623 (1970) · Zbl 0193.39203
[13] Lions, J.L., Magenes, E.: Probl?mes aux limites non homog?nes et applications, Vol. 1. Paris: Dunod 1968 · Zbl 0165.10801
[14] Nirenberg, L.: An application of generalized degree to a class of nonlinear problems. In: Troisi?me Colloque sur l’Analyse Fonctionnelle (Li?ge 1971), Centre Belge Recherches Math?matiques. pp. 57-74. Louvain: Vander 1971
[15] Rabinowitz, P.H.: A global theorem for nonlinear eigenvalue problems and applications. In: Contributions to Nonlinear Functional Analysis (Madison 1971). H. Zarantonello, ed. New York-London: Academic Press 1971 · Zbl 0271.47020
[16] Rabinowitz, P.H.: A note on a nonlinear elliptic equation. Indiana Univ. Math. J.22, 43-49 (1972) · Zbl 0241.35028 · doi:10.1512/iumj.1972.22.22006
[17] Shaw, H.: A nonlinear boundary value problem. In Nonlinear Functional Analysis and Differential Equations (East Lansing 1975), L. Cesari, R. Kannan, and J.D. Schuur, eds., pp. 339-346. New York-Basel: M. Dekker, Inc. 1976
[18] Schechter, M.: A nonlinear elliptic boundary value problem. Ann. Scuola norm. sup. Pisa, Sci. fis. mat., III. Ser.27, 707-716 (1973) · Zbl 0302.35044
[19] Whyburn, G.T.: Topological Analysis. Princeton: Princeton University Press 1958 · Zbl 0080.15903
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