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Bemerkungen über nichtlineare Störungen von Schrödinger-Operatoren. (German) Zbl 0323.35031


MSC:

35J60 Nonlinear elliptic equations
35J10 Schrödinger operator, Schrödinger equation
47J05 Equations involving nonlinear operators (general)
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References:

[1] AGMON, S.: Lectures on elliptic boundary value problems. Princeton, Toronto, New York, London: D. Van Nostrand 1965. · Zbl 0142.37401
[2] BRÉZIS, H.: Perturbations non linéaires d’opérateurs maximaux monotones. C.R. Acad. Sc. Paris269, 566-569 (1969). · Zbl 0182.19001
[3] BROWDER, F.E.: Existence theory for boundary value problems for quasilinear elliptic systems with strongly nonlinear lower order terms. Proc. Sympos. Pure Math., vol. XXIII, 269-286, Amer. Math. Soc., Providence, R.I. 1973.
[4] HESS, P.: Perturbations non linéaires d’opérateurs de Schroedinger. C.R. Acad. Sc. Paris (erscheint demnächst).
[5] HESS, P.: On nonlinear mappings of monotone type with respect to two Banach spaces. J. Math. pures et appl.52, 13-26 (1973). · Zbl 0222.47019
[6] KATO, T.: Schrödinger operators with singular potentials. Israel J. Math.13, 135-148 (1972). · Zbl 0246.35025 · doi:10.1007/BF02760233
[7] KATO, T.: Perturbation theory for linear operators. Berlin, Heidelberg, New York: Springer 1966. · Zbl 0148.12601
[8] KRASNOSELS’KII, M.A.: Topological methods in the theory of nonlinear integral equations. Oxford, London, New York, Paris: Pergamon Press 1964.
[9] LIONS, J.L.: Quelques méthodes de résolution des problèmes aux limites non linéaires. Dunod Gauthiers-Villars: Paris 1969.
[10] SIMADER, C.G.: Bemerkungen über Schrödinger-Operatoren mit stark singulären Potentialen. Math. Z.138, 53-70 (1974). · Zbl 0317.35028 · doi:10.1007/BF01221884
[11] SIMADER, C.G.: Some remarks on weak solutions of nonlinear perturbed linear strongly elliptic partial differential equations. Erscheint in Proc. of the Royal Soc. Edinburgh.
[12] SIMON, B.: Essential self-adjointness of Schrödinger operators with positive potentials. Math. Ann.201, 211-220 (1973). · Zbl 0234.47027 · doi:10.1007/BF01427943
[13] TON, B.A.: Pseudo-monotone operators in Banach spaces and nonlinear elliptic equations. Math. Z.121, 243-252 (1971). · Zbl 0222.47018 · doi:10.1007/BF01111598
[14] WEBB, J.R.L.: On the Dirichlet problem for strongly non-linear operators in unbounded domains. J. London Math. Soc.10, 163-170 (1975). · Zbl 0316.35037 · doi:10.1112/jlms/s2-10.2.163
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