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Hartman-Stampacchia results for stably pseudomonotone operators and non-linear hemivariational inequalities. (English) Zbl 1184.49022

Summary: We are concerned with two classes of non-standard hemivariational inequalities. In the first case we establish a Hartman-Stampacchia type existence result in the framework of stably pseudomonotone operators. Next, we prove an existence result for a class of nonlinear perturbations of canonical hemivariational inequalities. Our analysis includes both the cases of compact sets and of closed convex sets in Banach spaces. Applications to non-coercive hemivariational and variational-hemivariational inequalities illustrate the abstract results of this article.

MSC:

49J53 Set-valued and variational analysis
35J87 Unilateral problems for nonlinear elliptic equations and variational inequalities with nonlinear elliptic operators
47H05 Monotone operators and generalizations
47N10 Applications of operator theory in optimization, convex analysis, mathematical programming, economics
49J50 Fréchet and Gateaux differentiability in optimization
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[1] Fichera G, Mem. Acad. Naz. Lincei 7 pp 91– (1964)
[2] DOI: 10.1002/cpa.3160200302 · Zbl 0152.34601 · doi:10.1002/cpa.3160200302
[3] DOI: 10.1007/BF02392210 · Zbl 0142.38102 · doi:10.1007/BF02392210
[4] Panagiotopoulos PD, Hemivariational Inequalities: Applications to Mechanics and Engineering (1993)
[5] Panagiotopoulos PD, Acta Mechanica 42 pp 160– (1983)
[6] Panagiotopoulos PD, Topics in Nonsmooth Mechanics pp 75– (1988)
[7] Panagiotopoulos PD, Inequality Problems in Mechanics and Applications. Convex and Nonconvex Energy Functionals (1985) · doi:10.1007/978-1-4612-5152-1
[8] Naniewicz Z, Mathematical Theory of Hemivariational Inequalities and Applications (1995)
[9] Motreanu D, Nonconvex Optimization and its Applications, Vol. 29 (1999)
[10] Motreanu D, Variational and Non-Variational Methods in Nonlinear Analysis and Boundary Value Problems (2003)
[11] Clarke FH, Optimization and Nonsmooth Analysis (1983)
[12] DOI: 10.1017/S1446788700014609 · Zbl 1170.90498 · doi:10.1017/S1446788700014609
[13] DOI: 10.1016/S0893-9659(04)90089-4 · Zbl 1060.49004 · doi:10.1016/S0893-9659(04)90089-4
[14] DOI: 10.1016/j.jmaa.2006.07.063 · Zbl 1124.49005 · doi:10.1016/j.jmaa.2006.07.063
[15] DOI: 10.1016/0022-247X(87)90198-3 · Zbl 0644.47050 · doi:10.1016/0022-247X(87)90198-3
[16] DOI: 10.1023/A:1008340210469 · Zbl 0951.49018 · doi:10.1023/A:1008340210469
[17] Gwinner J, Variational Inequalities and Network Equilibrium Problems pp 123– (1979)
[18] DOI: 10.1080/01630560008816991 · Zbl 0981.49009 · doi:10.1080/01630560008816991
[19] DOI: 10.1007/BFb0079943 · doi:10.1007/BFb0079943
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