Rocky Mountain Journal of Mathematics

Infinitely Many Radial and Non-Radial Solutions for a Class of Hemivariational Inequalities

Alexandru Kristály

Full-text: Open access

Article information

Source
Rocky Mountain J. Math., Volume 35, Number 4 (2005), 1173-1190.

Dates
First available in Project Euclid: 5 June 2007

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1181069682

Digital Object Identifier
doi:10.1216/rmjm/1181069682

Mathematical Reviews number (MathSciNet)
MR2178983

Zentralblatt MATH identifier
1088.49004

Keywords
Hemivariational inequalities principle of symmetric criticality locally Lipschitz functions Palais-Smale condition radial and non-radial solutions

Citation

Kristály, Alexandru. Infinitely Many Radial and Non-Radial Solutions for a Class of Hemivariational Inequalities. Rocky Mountain J. Math. 35 (2005), no. 4, 1173--1190. doi:10.1216/rmjm/1181069682. https://projecteuclid.org/euclid.rmjm/1181069682


Export citation

References

  • D. Anderson and G. Derrick, Stability of time dependent particle like solutions in nonlinear field theories, J. Math. Phys. 11 (1970), 1336-1346.
  • T. Bartsch, Infinitely many solutions of a symmetric Dirichlet problem, Nonlinear Analysis TMA 20 (1993), 1205-1216.
  • --------, Topological methods for variational problems with symmetries, Springer-Verlag, Berlin, 1993.
  • T. Bartsch and Z.-Q. Wang, Existence and multiplicity results for some superlinear elliptic problems in $\r^N$, Comm. Partial Differential Equations 20 (1995), 1725-1741.
  • T. Bartsch and M. Willem, Infinitely many non-radial solutions of an Euclidean scalar field equation, J. Funct. Anal. 117 (1993), 447-460.
  • --------, Infinitely many radial solutions of a semilinear elliptic problem in $\r^N$, Arch. Rational Mech. Anal. 124 (1993), 261-276.
  • H. Berestycki and P.L. Lions, Nonlinear scalar field equations, Arch. Rational Mech. Anal. 82 (1983), 313-376.
  • K.-C. Chang, Variational methods for non-differentiable functionals and their applications to partial differential equations, J. Math. Anal. Appl. 80 (1981), 102-129.
  • F.H. Clarke, Nonsmooth analysis and optimization, Wiley, New York, 1983.
  • S. Coleman, V. Glazer and A. Martin, Action minima among solutions to a class of Euclidean scalar field equations, Comm. Math. Phys. 58 (1978), 211-221.
  • F. Gazzola and V. Rădulescu, A nonsmooth critical point theory approach to some nonlinear elliptic equations in $\r^N$, Differential Integral Equations 13 (2000), 47-60.
  • B. Gidas, W.-M. Ni and L. Nirenberg, Symmetry of positive solutions of nonlinear elliptic equations in $\r^N$, Adv. Math. Supp. Studies 7 (1981), 369-402.
  • 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. Math. 20 (1990), 1041-1049.
  • P.-L. Lions, Symétrie et compacité dans les espaces de Sobolev, J. Funct. Anal. 49 (1982), 315-334.
  • D. Motreanu and P.D. Panagiotopoulos, Minimax theorems and qualitative properties of the solutions of hemivariational inequalities, Kluwer Acad. Publ., Dordrecht, 1999.
  • D. Motreanu and V. Rădulescu, Variational and Non-variational Methods in Nonlinear Analysis and Boundary Value Problems, Kluwer Acad. Publ., Boston, 2003 (in press).
  • D. Motreanu and Cs. Varga, A nonsmooth equivariant minimax principle, Comm. Appl. Anal. 3 (1999), 115-130.
  • Z. Naniewicz and P.D. Panagiotopoulos, Mathematical theory of hemivariational inequalities and applications, Marcel Dekker, New York, 1995.
  • R.S. Palais, The principle of symmetric criticality, Comm. Math. Phys. 69 (1979), 19-30.
  • P.D. Panagiotopoulos, Hemivariational inequalities: Applications to mechanics and engineering, Springer-Verlag, New-York, 1993.
  • --------, Inequality problems in mechanics and applications. Convex and nonconvex energy functionals, Birkhäuser-Verlag, Basel, 1985.
  • P.H. Rabinowitz, Minimax methods in critical point theory with applications to differential equations, CBMS Regional Conf. Ser. in Math., Vol. 65, Amer. Math. Soc., Providence, RI, 1986.
  • --------, On a class of nonlinear Schrödinger equations, Z. Angew. Math. Phys. 43 (1992), 270-291.
  • W.A. Strauss, Existence of solitary waves in higher dimensions, Comm. Math. Phys. 55 (1977), 149-162.
  • M. Struwe, Multiple solutions of differential equations without Palais-Smale condition, Math. Ann. 261 (1982), 399-412.
  • M. Willem, Minimax theorems, Birkhäuser, Basel, 1995.