Pseudomonotone operators and nonlinear elliptic boundary value problems

Nobuyuki KENMOCHI

doi:10.2969/jmsj/02710121

Nobuyuki KENMOCHI

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JOURNAL FREE ACCESS

1975 Volume 27 Issue 1 Pages 121-149

DOI https://doi.org/10.2969/jmsj/02710121

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Published: 1975 Received: January 11, 1974 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) H. Brezis, Équations et inéquations non linéaires dans les espaces vectoriels en dualité, Ann. Inst. Fourier, Grenoble, 18, 1 (1968), 115-175.
2) H. Brezis, Problèmes unilatéraux, J. Math. Pure Appl., 51 (1972), 1-168.
3) H. Brezis and G. Stampacchia, Sur la régularité de la solution d'inéquations elliptiques, Bull. Soc. Math. France, 96 (1968), 153-180.
4) F. E. Browder, Nonlinear maximal monotone operators in Banach spaces, Math. Ann., 175 (1968), 89-113.
5) F. E. Browder, Nonlinear variational inequalities and maximal monotone mappings in Banach spaces, Math. Ann., 183 (1969), 213-231.
6) F. E. Browder, Existence theorems for nonlinear partial differential equations, Global analysis, Proc. Symp. Pure Math. Amer. Math. Soc. 16 (1970), 1-60.
7) E. Gagliardo, Caratterizzazioni delle tracce sulla frontiera relative ad alcune classi di funzioni in n variabili, Rend. Sem. Mat. Univ. Padova, 27 (1957), 284-305.
8) N. Kenmochi, Nonlinear operators of monotone type in reflexive Banach spaces and nonlinear perturbations, Hiroshima Math. J., 4 (1974), 229-263.
9) N. Kenmochi, Some nonlinear parabolic variational inequalities and applications, in preparation.
10) N. Kenmochi, Nonlinear operators of monotone type and nonlinear variational inequalities, in preparation.
11) M. A. Krasnosel'skii, Topological methods in the theory of nonlinear integral equations, Pergamon Press, Oxford, 1964.
12) J. Leray and J. L. Lions, Quelques résultats de Visik sur les problèmes elliptiques non linéaires par les méthodes de Minty-Browder, Bull. Soc. Math. France, 93 (1965), 97-107.
13) J.L. Lions, Problèmes aux limites dans les équations aux dérivées partielles, Montréal Univ., 1962.
14) J. L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod Gauthier-Villars, Paris, 1969.
15) J. L. Lions, Partial differential inequalities, Russian Math. Surveys, 27, 2 (1972), 91-159.
16) J. L. Lions and E. Magenes, Problemi ai limiti non omogenei (III), Annali Scuola Norm. Sup. Pisa, 15 (1961), 41-107.
17) J. L. Lions and G. Stampacchia, Variational inequalities, Comm. Pure Appl. Math., 20 (1967), 493-519.
18) W. Littman, G. Stampacchia and H. F. Weinberger, Regular points for elliptic equations with discontinuous coefficients, Annali Scuola Norm. Sup. Pisa, 17 (1963), 45-79.
19) U. Mosco, Convergence of convex sets and of solutions of variational inequalities, Advances Math., 3 (1969), 510-585.
20) R. T. Rockafellar, Convex analysis, Princeton Univ. Press, 1969.
21) R. T. Rockafellar, On the maximality of nonlinear monotone operators, Trans. Amer. Math. Soc., 149 (1970), 75-83.
22) G. Stampacchia, Variational inequalities, Theory and applications of monotone operators, Proc. NATO Advanced Study Inst. Venice, (1969), 101-192.

Right : [1] H. Brezis, Équations et inéquations non linéaires dans les espaces vectoriels en dualité, Ann. Inst. Fourier, Grenoble, 18, 1 (1968), 115-175.
[2] H. Brezis, Problèmes unilatéraux, J. Math. Pure Appl., 51 (1972), 1-168.
[3] H. Brezis and G. Stampacchia, Sur la régularité de la solution d'inéquations elliptiques, Bull. Soc. Math. France, 96 (1968), 153-180.
[4] F. E. Browder, Nonlinear maximal monotone operators in Banach spaces, Math. Ann., 175 (1968), 89-113.
[5] F. E. Browder, Nonlinear variational inequalities and maximal monotone mappings in Banach spaces, Math. Ann., 183 (1969), 213-231.
[6] F. E. Browder, Existence theorems for nonlinear partial differential equations, Global analysis, Proc. Symp. Pure Math. Amer. Math. Soc. 16 (1970), 1-60.
[7] E. Gagliardo, Caratterizzazioni delle tracce sulla frontiera relative ad alcune classi di funzioni in n variabili, Rend. Sem. Mat. Univ. Padova, 27 (1957), 284-305.
[8] N. Kenmochi, Nonlinear operators of monotone type in reflexive Banach spaces and nonlinear perturbations, Hiroshima Math. J., 4 (1974), 229-263.
[9] N. Kenmochi, Some nonlinear parabolic variational inequalities and applications, in preparation.
[10] N. Kenmochi, Nonlinear operators of monotone type and nonlinear variational inequalities, in preparation.
[11] M. A. Krasnosel'skii, Topological methods in the theory of nonlinear integral equations, Pergamon Press, Oxford, 1964.
[12] J. Leray and J. L. Lions, Quelques résultats de Visik sur les problèmes elliptiques non linéaires par les méthodes de Minty-Browder, Bull. Soc. Math. France, 93 (1965), 97-107.
[13] J. L. Lions, Problèmes aux limites dans les équations aux dérivées partielles, Montréal Univ., 1962.
[14] J. L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod Gauthier-Villars, Paris, 1969.
[15] J. L. Lions, Partial differential inequalities, Russian Math. Surveys, 27, 2 (1972), 91-159.
[16] J. L. Lions and E. Magenes, Problemi ai limiti non omogenei (III), Annali Scuola Norm. Sup. Pisa, 15 (1961), 41-107.
[17] J. L. Lions and G. Stampacchia, Variational inequalities, Comm. Pure Appl. Math., 20 (1967), 493-519.
[18] W. Littman, G. Stampacchia and H. F. Weinberger, Regular points for elliptic equations with discontinuous coefficients, Annali Scuola Norm. Sup. Pisa, 17 (1963), 45-79.
[19] U. Mosco, Convergence of convex sets and of solutions of variational inequalities, Advances Math., 3 (1969), 510-585.
[20] R. T. Rockafellar, Convex analysis, Princeton Univ. Press, 1969.
[21] R. T. Rockafellar, On the maximality of nonlinear monotone operators, Trans. Amer. Math. Soc., 149 (1970), 75-83.
[22] G. Stampacchia, Variational inequalities, Theory and applications of monotone operators, Proc. NATO Advanced Study Inst. Venice, (1969), 101-192.

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