References
- Gazzola F, Grunau H, Sweers G. Polyharmonic boundary value problems. Positivity preserving and nonlinear higher order elliptic equations in bounded domains. Berlin: Springer-Verlag; 2010.
- Brezis H, Nirenberg L. Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents. Commun Pure Appl Math. 1983;36:437–477.
- Cerami G, Solimini S, Struwe M. Some existence results for superlinear elliptic boundary value problems involving critical exponents. J Funct Anal. 1986;69:289–306.
- Lazzo M. Solutions positives multiples pour une équation elliptique non linéaire avec l’exposant critique de Sobolev. C R Acad Sci Paris. 1992;314(Série I):61–64.
- Castro A, Clapp M. The effect of the domain topology on the number of minimal nodal solutions of an elliptic equation at critical growth in a symmetric domain. Nonlinearity. 2003;16:579–590.
- Cano A, Clapp M. Multiple positive and 2-nodal symmetric solutions of elliptic problems with critical nonlinearity. J Differ Equ. 2003;193:133–158.
- Swanson CA. Uniqueness for semilinear polyharmonic problems. Nonlinear Anal. 1995;25:1055–1062.
- Swanson CA, Yu LS. Radial polyharmonic problems in ℝN. J Math Anal Appl. 1993;174:461–466.
- Bachar I, Zribi M. Existence results for some polyharmonic problems in the half-space. J Math Anal Appl. 2006;322:610–620.
- Bartsch T, Weth T, Willem M. A Sobolev inequality with remainder term and critical equations on domanins with topology for the polyharmonic operator. Calc Var PDE. 2003;18:253–268.
- Ge Y. Positive solutions in semilinear critical problems for polyharmonic operators. J Math Pures Appl. 2005;84:199–245.
- Ge Y, Wei J, Zhou F. A critical elliptic problem for polyharmonic operators. J Funct Anal. 2011;260:2247–2282.
- Pucci P, Serrin J. A general variational identity. Indiana Univ Math J. 1986;35:681–703.
- Pucci P, Serrin J. Critical exponents and critical dimensions for polyharmonic operators. J Math Pures Appl. 1990;69:55–83.
- Grunau H. Positive solutions to semilinear polyharmonic Dirichlet problems involving critical Sobolev exponents. Calc Var PDE. 1995;3:243–252.
- Bartsch T, Schneider M, Weth T. Multiple solutions of critical polyharmonic equation. J Reine Angew Math. 2004;571:131–143.
- Dou J, Guo Q. Solutions for polyharmonic elliptic problems with critical nonlinearities in symmetric domains. Commun Pure Appl Anal. 2012;11:453–464.
- Brezis H. Functional analysis, Sobolev spaces and partial differential equations. New York (NY): Springer; 2010.
- Willem M. Minimax theorems. Boston-Basel-Berlin: Birkhäuser PNLDE; 1996.
- Swanson CA. The best Sobolev constant. Applicable Anal. 1992;47:227–239.
- Palais R. The principle of symmetric criticality. Commun Math Phys. 1979;69:19–30.
- Struwe M. A global compactness result for elliptic boundary value problems involving limiting nonlinearities. Math Z. 1984;187:511–517.
- Struwe M. Variational methods. 4th ed. Berlin-Heidelberg: Springer-Verlage; 2008.
- Clapp M, Puppe D. Critical point theory with symmetries. J Reine Angew Math. 1991;418:1–29.