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EXISTENCE AND MULTIPLICITY OF NONTRIVIAL SOLUTIONS FOR DEGENERATE HEMIVARIATIONAL INEQUALITIES INVOLVING LERAY–LIONS TYPE OPERATOR WITH CRITICAL GROWTH

KAIMIN TENG

Department of Mathematics, Taiyuan University of Technology, Taiyuan, Shanxi 030024, P. R. China

https://doi.org/10.1142/S0219530513500073Cited by:0 (Source: Crossref)

Abstract

In this paper, we investigate a hemivariational inequality involving Leray–Lions type operator with critical growth. Some existence and multiple results are obtained through using the concentration compactness principle of P. L. Lions and some nonsmooth critical point theorems.

Keywords:

AMSC: 34C25, 58E30, 47H04

References

J. G. Azorero and I. P. Alonso , Trans. Amer. Math. Soc. 323 , 877 ( 1991 ) . Crossref, Web of Science, Google Scholar
H. Brézis and L. Nirenberg , Comm. Pure Appl. Math. 36 , 437 ( 1983 ) . Crossref, Web of Science, Google Scholar
J. Chabrowski , J. Fixed Point Theory Appl. 4 , 137 ( 2008 ) . Crossref, Web of Science, Google Scholar
K. Chang , J. Math. Anal. Appl. 80 , 102 ( 1981 ) . Crossref, Web of Science, Google Scholar
D. C. Clark , Indiana Univ. Math. J. 22 , 65 ( 1972 ) . Crossref, Web of Science, Google Scholar
F. Clarke , Optimization and Nonsmooth Analysis ( Wiley , New York , 1983 ) . Google Scholar
M. Fang , J. Differential Equations 232 , 441 ( 2007 ) . Crossref, Web of Science, Google Scholar
M. E. Filippakis , L. Gasinki and N. Papageorgiou , Nonlinear Anal. 56 , 331 ( 2004 ) . Crossref, Web of Science, Google Scholar
L. Gasinki and N. Papageorgiou , Funk. Ekva. 43 , 271 ( 2000 ) . Google Scholar
L. Gasinki and N. Papageorgiou , Nonsmooth Critical Point Theory and Nonlinear Boundary Value Problems ( Chapman Hall/CRC , Boca Raton , 2005 ) . Google Scholar
L. Gasinki and N. S. Papageorgiou , Adv. Nonlinear Stud. 8 , 843 ( 2008 ) . Crossref, Web of Science, Google Scholar
N. Ghoussoub and C. Yuan , Trans. Amer. Math. Soc. 352 , 5703 ( 2000 ) . Crossref, Web of Science, Google Scholar
J. Heinonen , T. Kilpelänen and O. Martio , Nonlinear Potential Theory of Degenerate Elliptic Equations ( Oxford University Press , Oxford , 1993 ) . Google Scholar
S. Hu and N. S. Papageorgiou , Handbook of Multivalued Analysis I ( Kluwer Academic , 1997 ) . Crossref, Google Scholar
N. C. Kourogenis and N. S. Papageorgiou , J. Austral. Math. Soc. 69 , 245 ( 2000 ) . Crossref, Web of Science, Google Scholar
S. Th. Kyritsi , D. O'Regan and N. S. Papageorgiou , Adv. Nonlinear Stud. 9 , 453 ( 2009 ) . Crossref, Web of Science, Google Scholar
S. Th. Kyritsi and N. S. Papageorgiou , Calc. Var. 20 , 1 ( 2004 ) . Crossref, Web of Science, Google Scholar
V. K. Le and K. Schmitt , J. Differential Equations 114 , 170 ( 1998 ) . Crossref, Web of Science, Google Scholar
J. Leray and J. L. Lions , Bull. Soc. Math. France 93 , 97 ( 1965 ) . Crossref, Google Scholar
S. Li and W. Zou , Nonlinear Anal. 12 , 769 ( 1998 ) . Google Scholar
P. Lindqvist , Proc. Amer. Math. Soc. 109 , 157 ( 1990 ) . Web of Science, Google Scholar
P. L. Lions, Rev. Mat. Iberoamericana 1(1), 145 (1985). Crossref, Google Scholar
P. L. Lions, Rev. Mat. Iberoamericana 1(2), 45 (1985). Crossref, Google Scholar
R. Livrea and S. A. Marano , Adv. Differential Equations 9 , 961 ( 2004 ) . Crossref, Web of Science, Google Scholar
D. Motreanu and P. D. Panagiotopoulos , Minimax Theorems and Qualitative Properties of the Solutions of Hemivariational Inequalities ( Kluwer Academic Publishers , 1999 ) . Crossref, Google Scholar
D. Motreanu , V. V. Motreanu and N. S. Papageorgiou , Trans. Amer. Math. Soc. 360 , 2527 ( 2008 ) . Crossref, Web of Science, Google Scholar
Z. Naniewicz and P. Panagiotopoulos , Mathematical Theory of Hemivariational Inequalities and Applications ( Marcel Dekker , 1995 ) . Google Scholar
N. S. Papageorgiou , E. M. Rocha and V. Staicu , Nonlinear Anal. 69 , 1150 ( 2009 ) . Crossref, Web of Science, Google Scholar
E. A. B. Silva and M. S. Xavier , Ann. Inst. H. Poincaré Anal. Non Linéaire 20 , 341 ( 2003 ) . Crossref, Web of Science, Google Scholar
K. Teng and X. Wu , Nonlinear Anal. 68 , 1652 ( 2008 ) . Crossref, Web of Science, Google Scholar
K. Teng and X. Wu , Nonlinear Anal. 68 , 3742 ( 2008 ) . Crossref, Web of Science, Google Scholar
K. Teng , J. Glob. Optim. 46 , 89 ( 2010 ) . Crossref, Web of Science, Google Scholar
P. Tolksdorf , J. Differential Equations 51 , 126 ( 1984 ) . Crossref, Web of Science, Google Scholar
M. Willem , Minimax Theorems ( Birkhäuser , 1996 ) . Crossref, Google Scholar
J. F. Yang , Nonlinear Anal. 25 , 1283 ( 1995 ) . Crossref, Web of Science, Google Scholar
X. Zhu , Sci. Sinica Ser. A 31 , 1166 ( 1988 ) . Google Scholar