Abstract
Using the principle of symmetric criticality for Motreanu–Panagiotopoulos type functionals we give some existence and multiplicity results for a class of variational–hemivariational inequalities on \(\mathbb {R}\) L+M.
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Adams, R.A. (1975), Sobolev Spaces, Academic Press.
Bartsch T., Liu Z., Weth T. (2004), Sign changing solutions of superlinear Schrödinger equations. Comm. Partial Diff. Equations 29 (1–2): 25–42
Bartsch T., Pankov A., Wang Z.-Q. (2001), Nonlinear Schrödinger equations with steep potential well. Comm. Contemp. Math. 4, 549–569
Bartsch T., Wang Z.-Q. (1995), Existence and multiplicity results for some superlinear elliptic problems in \(\mathbb{R}\) N. Comm. Partial Diff. Equations 20, 1725–1741
Bartsch T., Willem M. (1993), Infinitely many non-radial solutions of an Euclidean scalar field equation. J. Func. Anal. 117, 447–460
Bartsch T., Willem M. (1993), Infinitely many radial solutions of a semilinear elliptic problem on R N. Arch. Rational Mech. Anal. 124(3): 261–276
Brezis, H. (1992), Analyse functionelle. Theorie et applications. Masson.
Browder F.E. (1964), Les problèmes non-linéares. Les Presses de l’Université de, Montréal
Clarke, F.H. (1983), Optimization and Nonsmooth Analysis. Wiley.
Dályai Zs., Varga Cs. (2004), An existence result for hemivariational inequalities. Electronic J. Differential Equations 37, 1–17
Gasiński L., Papageorgiou N.S. (2005), Nonsmooth critical point theory and nonlinear boundary value problems, Series in Mathematical Analysis and Applications, 8. Chapman & Hall/CRC, Boca Raton, FL
Gazzola F., Rădulescu V. (2000), A nonsmooth critical point theory approach to some nonlinear elliptic equations in \(\mathbb {R}\) n. Diff. Integral Equations 13, 47–60
Krawcewicz W., Marzantowicz W. (1990), Some remarks on the Lusternik- Schnirelman method for non-differentiable functionals invariant with respect to a finite group action. Rocky Mountain J. Math. 20, 1041–1049
Kobayashi J., Ôtani M. (2004), The principle of symmetric criticality for non-differentiable mappings. J. Funct. Anal. 214, 428–449
Kourogenis N.C., Papadrianos J., Papageorgiou, N.S. (2002), Extensions of nonsmooth critical point theory and applications. Atti Sem. Mat. Fis. Univ. Modena, L, 381–414.
Kristály A. (2005), Infinitely many radial and non-radial solutions for a class of hemivariational inequalities. Rocky Mountain J. Math. 35, 1173–1190
Kristály A. (2005), Multiplicity results for an eigenvalue problem for hemivariational inequalities in strip-like domains. Set-Valued Anal. 13, 85–103
Kristály, A., Varga, C. and Varga, V. A nonsmooth principle of symmetric criticality and variational-hemivariational inequalities. Journal of Mathematical Analysis and Applications (to appear).
Marano S., Motreanu D. (2002), On a three critical points theorem for non-differentiable functions and applications to nonlinear boundary value problems. Nonlinear Anal. 48, 37–52
Motreanu D., Panagiotopoulos P.D. (1999), Minimax Theorems and Qualitative Properties of the Solutions of Hemivariational Inequalities. Kluwer Academic Publishers, Dordrecht
Motreanu, D. and Rădulescu, V. (2003), Variational and non-variational methods in nonlinear analysis and boundary value problems. Nonconvex Optimization and its Applications, 67. Kluwer Academic Publishers, Dordrecht.
de Morais Filho D.C., Souto M.A.S., Marcos Do J. (2000), A compactness embedding lemma, a principle of symmetric criticality and applications to elliptic problems. Proyecciones, Universidad Catolica del Norte, Antofagasta–Chile 19(1): 1–17
Naniewicz Z., Panagiotopoulos P.D. (1995), Mathematical Theory of Hemivariational Inequalities and Applications. Marcel Dekker, New York
De Nápoli P., Mariani M.C. (2003), Mountain pass solutions to equations of p-Laplacian type. Nonlinear Analysis 54, 1205–1219
Palais R.S. (1979), The principle of symmetric criticality. Comm. Math. Phys. 69, 19–30
Panagiotopoulos P.D. (1993), Hemivariational Inequalities: Applications to Mechanics and Engineering. Springer, New York
Ricceri B. (2000), Existence of three solutions for a class of elliptic eigenvalue problems. Math. Comput. Modelling, 32, 1485–1494
Strauss W.A. (1977), Existence of solitary waves in higher dimensions. Comm. Math. Phys. 55, 149–162
Szulkin A. (1986), Minimax methods for lower semicontinuous functions and applications to nonlinear boundary value problems. Ann. Inst. Henri Poincaré 3, 77–109
Varga Cs. (2005), Existence and infinitely many solutions for an abstract class of hemivariational inequalities. J. Inequalities Appl. 9(2): 89–107
Willem M. (1996), Minimax Theorems. Birkhäuser, Boston
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This work was partially supported by MEdC-ANCS, research project CEEX 2983/11.10.2005.
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Lisei, H., Varga, C. Some Applications to Variational–Hemivariational Inequalities of the Principle of Symmetric Criticality for Motreanu–Panagiotopoulos Type Functionals. J Glob Optim 36, 283–305 (2006). https://doi.org/10.1007/s10898-006-9009-0
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DOI: https://doi.org/10.1007/s10898-006-9009-0