A multiplicity result for gradient-type systems with non-differentiable term

Acta Mathematica Hungarica

Volumn 118, Issue 1-2, 2008, Pages 85-104

  Breckner, B E ^a   Varga, Cs ^a  

^a BABE BOLYAI UNIVERSITY   (Romania)

Author keywords

Generalized directional derivative; Locally Lipschitz function; Principle of symmetric criticality; Systems of hemivariational inequalities

Indexed keywords

EID: 43249096941     PISSN: 02365294     EISSN: 15882632     Source Type: Journal    
DOI: 10.1007/s10474-007-6165-8     Document Type: Article

References (15)

1. [1] T. Bartsch D. G. Figueiredo de 1999 Infinitely many solutions of nonlinear elliptic systems Progr. Nonlinear Differential Equations Appl. 35 51 67 T. Bartsch and D. G. de Figueiredo, Infinitely many solutions of nonlinear elliptic systems, Progr. Nonlinear Differential Equations Appl., 35 (1999), 51–67.
2. [2] T. Bartsch Z. Q. Wang 1995 Existence and multiplicity results for some superlinear elliptic problems on R N Comm. Partial Differential Equations 20 1725 1741 0837.35043 10.1080/03605309508821149 1349229 T. Bartsch and Z. Q. Wang, Existence and multiplicity results for some superlinear elliptic problems on R N, Comm. Partial Differential Equations, 20 (1995), 1725–1741.
3. [3] F. H. Clarke 1983 Nonsmooth Analysis John Wiley & Sons New York etc. 0582.49001 F. H. Clarke, Nonsmooth Analysis, John Wiley & Sons (New York etc., 1983).
4. [4] D. G. Costa 1994 On a class of elliptic systems in R N Electron. J. Differential Equations 111 103 122 0803.35052 10.1006/jdeq.1994.1077 D. G. Costa, On a class of elliptic systems in R N, Electron. J. Differential Equations, 111 (1994), 103–122.
5. [5] T.-L. Dinu 2006 Entire solutions of Schrödinger elliptic systems with discontinuous nonlinearity and sign-changing potential Math. Modelling and Analysis 11 1 14 2268125 T.-L. Dinu, Entire solutions of Schrödinger elliptic systems with discontinuous nonlinearity and sign-changing potential, Math. Modelling and Analysis, 11 (2006), 1–14.
6. [6] N. V. Efimov S. B. Stechkin 1961 Approximate compactness and Chebyshev sets Soviet Math. Dokl. 2 1226 1228 N. V. Efimov and S. B. Stechkin, Approximate compactness and Chebyshev sets, Soviet Math. Dokl., 2 (1961), 1226–1228.
7. [7] W. Krawcewicz W. Marzantowicz 1990 Some remarks on the Lusternik-Schnirelman method for non-differentiable functionals invariant with respect to a finite group action Rocky Mountain J. of Math. 20 1041 1049 0728.58005 1096570 10.1216/rmjm/1181073061 W. Krawcewicz and W. Marzantowicz, Some remarks on the Lusternik-Schnirelman method for non-differentiable functionals invariant with respect to a finite group action, Rocky Mountain J. of Math., 20 (1990), 1041–1049.
8. [8] A. Kristály 2006 Existence of nonzero weak solutions for a class of elliptic variational inclusions systems in R N Nonlinear Analysis 65 1578 1594 05047622 10.1016/j.na.2005.10.033 2248686 A. Kristály, Existence of nonzero weak solutions for a class of elliptic variational inclusions systems in R N, Nonlinear Analysis, 65 (2006), 1578–1594.
9. [9] A. Kristály Cs. Varga 2004 An Introduction to Critical Point Theory for Non-smooth Functions Casa Cărţii de Ştiinţă Cluj-Napoca A. Kristály and Cs. Varga, An Introduction to Critical Point Theory for Non-smooth Functions, Casa Cărţii de Ştiinţă (Cluj-Napoca, 2004).
10. [10] P. L. Lions 1982 Symétrie et compacité dans les espaces de Sobolev J. Funct. Anal. 49 312 334 10.1016/0022-1236(82)90072-6 P. L. Lions, Symétrie et compacité dans les espaces de Sobolev, J. Funct. Anal., 49 (1982), 312–334.
11. [11] D. Motreanu P. D. Panagiotopoulos 1999 Minimax Theorems and Qualitative Properties of the Solutions of Hemivariational Inequalities, Nonconvex Optimization and its Application, 29 Kluwer Academic Publishers Dordrecht D. Motreanu and P. D. Panagiotopoulos, Minimax Theorems and Qualitative Properties of the Solutions of Hemivariational Inequalities, Nonconvex Optimization and its Application, 29, Kluwer Academic Publishers (Dordrecht, 1999).
12. [12] D. Motreanu Cs. Varga 1999 A nonsmooth equivariant minimax principle Commun. Appl. Anal. 3 115 130 0922.49003 1669749 D. Motreanu and Cs. Varga, A nonsmooth equivariant minimax principle, Commun. Appl. Anal., 3 (1999), 115–130.
13. [13] B. Ricceri 2001 A further improvement of a minimax theorem of Borenshtein and Shul’man J. Nonlinear Conver Anal. 2 279 283 1045.49002 1848707 B. Ricceri, A further improvement of a minimax theorem of Borenshtein and Shul’man, J. Nonlinear Conver Anal., 2 (2001), 279–283.
14. [14] B. Ricceri 2005 A general multiplicity theorem for certain nonlinear equations in Hilbert spaces Proc. Amer. Math. Soc. 133 3255 3261 1069.47068 10.1090/S0002-9939-05-08218-3 2161147 B. Ricceri, A general multiplicity theorem for certain nonlinear equations in Hilbert spaces, Proc. Amer. Math. Soc., 133 (2005), 3255–3261.
15. [15] I. G. Tsar’kov 2004 Nonunique solvability of certain differential equations and their connection with geometric approximation theory Math. Notes 75 259 271 1110.47313 10.1023/B:MATN.0000015042.89501.ed 2054560 I. G. Tsar’kov, Nonunique solvability of certain differential equations and their connection with geometric approximation theory, Math. Notes, 75 (2004), 259–271.