### Group Actions On The Sphere And Multiplicity Results For The Cr-Yamabe Equation

#### Abstract

#### Keywords

#### Full Text:

PDF (English)#### References

A. Ambrosetti, P.H. Rabinowitz, Dual variational methods in critical point theory and applications, J. Functional Analysis 14 (1973), 349-381.

A. Bahri, S. Chanillo, The difference of topology at infinity in changing-sign Yamabe problems on S^{3} (the case of two masses), Comm. Pure Appl. Math. 54 (2001), no. 4, 450-478.

A. Bahri, Y. Xu, Recent progress in conformal geometry, ICP Advanced Texts in Mathematics, 1. Imperial College Press, London, 2007.

L.A. Caffarelli, B. Gidas, J. Spruck, Asymptotic symmetry and local behavior of semilinear elliptic equations with critical Sobolev growth, Comm. Pure Appl. Math. 42 (1989), no. 3, 271-297.

G. Citti, Semilinear Dirichlet Problem Involving Critical Exponent for the Kohn Laplacian, Ann. Mat. Pura Appl. (4) 169 (1995), 375-392.

M. del Pino, M. Musso, F. Pacard, A. Pistoia, Torus action on S^{n} and sign changing solutions for conformally invariant equations, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 12 (2013), no. 1, 209-237.

M. del Pino, M. Musso, F. Pacard, A. Pistoia, Large energy entire solutions for the Yamabe equation, J. Differential Equations 251 (2011), no. 9, 2568-2597.

W.Y. Ding, On a conformally invariant elliptic equation on R^{n} , Comm. Math. Phys. 107 (1986), no. 2, 331-335.

G.B. Folland, E.M. Stein, Estimates for the ∂ ̄_{b} complex and analysis on the Heisenberg group, Comm. Pure Appl. Math. 27 (1974), 429-522.

N. Garofalo, E. Lanconelli, Existence and nonexistence results for semilinear equations on the Heisenberg group, Indiana Univ. Math. J. 41 (1992), no. 1, 71-98.

D. Jerison, J.M. Lee, The Yamabe problem on CR manifolds, J. Differential Geom. 25 (1987), no. 2, 167-197.

D. Jerison, J.M. Lee, Extremals for the Sobolev inequality on the Heisenberg group and the CR Yamabe problem, J. Amer. Math. Soc. 1 (1988), no. 1, 1-13.

N. Hirano, Multiplicity of solutions for nonhomogeneous nonlinear elliptic equations with critical exponents, Topol. Methods Nonlinear Anal. 18 (2001), 269-281.

T. Isobe, A perturbation method for spinorial Yamabe type equations on S^{m} and its application, Math. Ann. 355 (2013), no. 4, 1255-1299.

A. Maalaoui, Infinitely many solutions for the Spinorial Yamabe Problem on the Round Sphere, preprint

A. Maalaoui, V. Martino, Changing-sign solutions for the CR-Yamabe equation, Differential Integral Equations 25 (2012), no. 7-8, 601-609.

A. Maalaoui, V. Martino, Existence and Concentration of Positive Solutions for a Super-critical Fourth Order Equation, Nonlinear Anal. 75 (2012), 5482-5498

A. Maalaoui, V. Martino, Existence and Multiplicity Results for a non-Homogeneous Fourth Order Equation, Topol. Methods Nonlinear Anal. 40 (2012), no. 2, 273-300

A. Maalaoui, V. Martino, Multiplicity result for a nonhomogeneous Yamabe type equation involving the Kohn Laplacian, J. Math. Anal. Appl. 399 (2013), no. 1, 333-339

A. Maalaoui, V. Martino, A. Pistoia, Concentrating Solutions for a Sub-Critical Sub-Elliptic Problem, Differential and Integral Equations 26 (2013), no. 11-12, 1263-1274

A. Maalaoui, V. Martino, G. Tralli, Complex group actions on the sphere and sign changing solutions for the CR-Yamabe equation, J. Math. Anal. Appl., 431, (2015), 126-135

R.S. Palais, The principle of symmetric criticality, Comm. Math. Phys. 69 (1979), no. 1, 19-30.

N. Saintier, Changing sign solutions of a conformally invariant fourth-order equation in the Euclidean space, Comm. Anal. Geom. 14 (2006), no. 4, 613-624.

DOI: 10.6092/issn.2240-2829/5975

### Refbacks

- There are currently no refbacks.

Copyright (c) 2015 Vittorio Martino

This work is licensed under a Creative Commons Attribution 3.0 Unported License.