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Maximal and minimal solutions of elliptic differential equations with discontinuous non-linearities. (English) Zbl 0403.35036


MSC:

35J60 Nonlinear elliptic equations
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
35R05 PDEs with low regular coefficients and/or low regular data

Citations:

Zbl 0345.47044
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References:

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[9] Hess, P.: On the solvability of non-linear elliptic boundary value problems. Indiana Univ. Math. J.25, 461-466 (1976) · Zbl 0329.35029
[10] Kolmogorov, A., Fomine, S.: Eléments de la théorie de fonctions et de l’analyse fonctionnelle. Moscou: Mir 1974 · Zbl 0299.46001
[11] Massabo, I., Stuart, C.A.: Elliptic eigenvalue problems with discontinuous non-linearities. J. Math. Anal. Appl. (to appear)
[12] Massabo, I.: Positive eigenvalues for elliptic equations with discontinuous non-linearities. Boll. Un. Mat. Ital. (to appear)
[13] Nistri, P.: Positive solutions of a non-linear eigenvalue problem with discontinuous non-linearity. Proc. Roy. Soc. Edinburgh (to appear) · Zbl 0437.34013
[14] Puel, J.P.: Sur des problèmes quasi-linéaires elliptiques et paraboliques d’ordre 2. C.R. Acad. Sci. Paris Sér. A275, 179-182 (1972) · Zbl 0241.35026
[15] Rauch, J.: Discontinuous semilinear differential equations and multiple valued maps. Proc. Amer. Math. Soc.64, 277-282 (1977) · Zbl 0413.35031
[16] Riesz, F., Sz-Nagy, B.: Functional Analysis. New York: Ungar 1955 · Zbl 0070.10902
[17] Stuart, C.A.: Differential equations with discontinuous non-linearities. Arch. Rational Mech. Anal.63, 59-75 (1976) · Zbl 0393.34010
[18] Stuart, C.A.: Boundary-value problems with discontinuous non-linearities. In: Ordinary and Partial Differential Equations. Proceedings of the Fourth Conference (Dundee, 1976). Lecture Notes in Mathematics564, pp. 472-484. Berlin-Heidelberg-New York: Springer 1976
[19] Stuart, C.A.: The number of solutions of boundary-value problems with discontinuous non-linearities. Arch. Rational Mech. Anal.66, 225-235 (1977) · Zbl 0388.34012
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