Rocky Mountain Journal of Mathematics

Some existence results for a class of fourth order elliptic equations with nonsmooth potential

Guoqing Zhang and Sanyang Liu

Full-text: Open access

Article information

Source
Rocky Mountain J. Math., Volume 40, Number 5 (2010), 1729-1743.

Dates
First available in Project Euclid: 16 November 2010

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1289916920

Digital Object Identifier
doi:10.1216/RMJ-2010-40-5-1729

Mathematical Reviews number (MathSciNet)
MR2737387

Zentralblatt MATH identifier
1205.35075

Keywords
Existence and multiplicity results nonsmooth functionals asymptotically linear local linking

Citation

Zhang, Guoqing; Liu, Sanyang. Some existence results for a class of fourth order elliptic equations with nonsmooth potential. Rocky Mountain J. Math. 40 (2010), no. 5, 1729--1743. doi:10.1216/RMJ-2010-40-5-1729. https://projecteuclid.org/euclid.rmjm/1289916920


Export citation

References

  • P. Bartolo, V. Benci and D. Fortunato, Abstract critical point theorems and applications to nonlinear problems with “strong” resonance at infinity, Nonlinear Anal. TMA 7 (1983), 981-1012.
  • K.C. Chang, Variational methods for nondifferentiable functionals and their applications to partial differential equations, J. Math. Anal. Appl. 80 (1981), 102-129.
  • F.H. Clarke, A new approach to Lagrange multipliers, Math. Oper. Res. 1 (1976), 165-174.
  • E. De Giorgi, G. Buttazzo and G. Dalmaso, On the lower semicontinuity of certain integral functionals, Atti. Accad. Naz. Lincei. Cl. Sci. Fis. Mat. Natur. Rend. Lincer 74 (1983), 274-282.
  • L. Gasinski and N. S. Papageorgiou, Nonsmooth critical point theory and nonlinear boundary value problems, Chapman and Hall/ CRC, Boca Raton, FL, 2005.
  • D. Gilbarg and N.S. Trudinger, Elliptic partial differential equations of second order, 2 -1983.
  • D. Kandilakis, N. Kourogenis and N.S. Papageorgiou, Two nontrivial critical points for nonlinear functionals via local linking and applications, J. Global Optim. 34 (2006), 219-244.
  • N. Kourogenis and N.S. Papageorgiou, Nonsmooth critical point theory and nonlinear elliptic equations at reaonance, J. Australian Math. Soc. 69 (2000), 245-271.
  • A. Kristaly, Infinitely many radial and non-radial solutions for a class of hemivaritional inequalities, Rocky Mountain J. Math. 35 (2005), 1173-1190.
  • G. Li and H. Zhou, Asymptotically linear Dirichlet problem for the $p$-Laplacian, Nonlinear Anal. TMA 43 (2001), 1043-1055.
  • A.M. Micheletti and A. Pistoia, Multiplicity results for a fourth-order semilinear elliptic problem, Nonlinear Anal. TMA 31 (1998), 895-908.
  • D. Motreanu and P.D. Panagiotopoulos, Minimax theorems and qualitative properties of the solutions of hemivariational inequalities, Kluwer Academic Publishers, Dordrecht, 1999.
  • D. Motreanu and Cs. Varga, A nonsmooth equivariant minimax principle, Comm. Appl. Anal. 3 (1999), 115-130.
  • G. Tarantello, A note on a semilinear elliptic problem, Differential and Integral Equations 5 (1992), 561-566.
  • J. Zhang, Existence results for some fourth-order nonlinear elliptic problems, Nonlinear Anal. TMA 45 (2001), 29-36.
  • J. Zhang and S. Li, Multiple nontrivial solutions for some fourth-order semilinear elliptic problems, Nonlinear Anal. TMA 60 (2005), 221-230.