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Existence theorems for a class of two point boundary problems. (English) Zbl 0295.35074


MSC:

35R20 Operator partial differential equations (= PDEs on finite-dimensional spaces for abstract space valued functions)
35K20 Initial-boundary value problems for second-order parabolic equations
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References:

[1] Barbu, V.: A class of boundary problems for second order abstract differential equations. J. fac. Sci. univ. Tokyo, sect. IA 19, 295-319 (1972) · Zbl 0256.47052
[2] Brézis, H.: Problèmes unilatéraux. J. math. Pures appl. 51, 202-263 (1972) · Zbl 0221.35028
[3] Brézis, H.: Monotonicity methods in Hilbert spaces and some applications to nonlinear partial differential equations. Contributions to nonlinear functional analysis, 101-156 (1971) · Zbl 0278.47033
[4] Brézis, H.: Équations d’évolution du second ordre associées à des opérateurs maximaux monotones. Israel J. Math. 12, 51-60 (1972) · Zbl 0248.47026
[5] Brézis, H.: Opérateurs maximaux monotones et semigroupes de contractions dans LES espaces de Hilbert. Mathematical studies 5 (1973) · Zbl 0252.47055
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[8] Lions, J. L.: Partial differential inequalities. Uspehi mat. Nauk. 26, 202-263 (1971)
[9] Lions, J. L.: Quelques problèmes de la théorie des équations nonlinéaires d’évolution. Problems in nonlinear analysis, 191-342 (1971)
[10] Moreau, J.: Fonctionelles convexes. Mimeographed lecture notes for séminaire sur LES équations aux dérivées partielles (1966–1967)
[11] N. Pavel, Nonlinear boundary value problems for second order differential equations, J. Math. Anal. Appl., in press.
[12] Rockafellar, R. T.: Convex functions, monotone operators and variational inequalities. Theory and applications of monotone operators, 35-66 (1969)
[13] Rockafellar, R. T.: Existence and duality theorems for convex problem of bolza. Trans. amer. Math. soc. 159, 1-40 (1971) · Zbl 0255.49007
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