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SYMMETRY OF COMPONENTS FOR RADIAL SOLUTIONS OF γ-LAPLACIAN SYSTEMS
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 Title & Authors
SYMMETRY OF COMPONENTS FOR RADIAL SOLUTIONS OF γ-LAPLACIAN SYSTEMS
Wang, Yun;
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 Abstract
In this paper, we give several sufficient conditions ensuring that any positive radial solution (u, v) of the following -Laplacian systems in the whole space has the components symmetry property Here n > , > 1. Thus, the systems will be reduced to a single -Laplacian equation: . Our proofs are based on suitable comparation principle arguments, combined with properties of radial solutions.
 Keywords
-Laplacian system;components symmetry property;radial solution;
 Language
English
 Cited by
 References
1.
J. Bourgain, Global solutions of Nonlinear Schrodinger Equations, Amer. Math. Soc. Colloq. Publ. 46 AMS, Providence, RI, 1999.

2.
J. Byeon, L. Jeanjean, and M. Maris, Symmetry and monotonicity of least energy solutions, Calc. Var. PDEs 36 (2009), no. 4, 481-492. crossref(new window)

3.
T. Cazenave, Semilinear Schrodinger equations, Courant Lecture Notes in Mathematics, 10. New York University, Courant Institute of Mathematical Sciences, New York; American Mathematical Society, Providence, RI, 2003.

4.
W. Chen and C. Li, Classification of solutions of some nonlinear elliptic equations, Duke Math. J. 63 (1991), no. 3, 615-622. crossref(new window)

5.
W. Chen and C. Li, Classification of positive solutions for nonlinear differential and integral systems with critical exponents, Acta Math. Sci. Ser. B Engl. Ed. 29 (2009), no. 4, 949-960.

6.
M. Franca, Classification of positive solutions of p-Laplace equation with a growth term, Arch. Math. (BRNO), 40 (2004), no. 4, 415-434.

7.
N. Kawano, E. Yanagida, and S. Yotsutani, Structure theorems for positive radial solutionsto div($\left|Du\right|^{m-2}$) + K($(\left|x\right|)u^q$ = 0 in ${\mathbb{R}}^n$, J. Math. Soc. Japan 45 (1993), no. 4, 719-742. crossref(new window)

8.
Y. Lei and C. Li, Integrability and asymptotics of positive solutions of a ${\gamma}$-Laplacian system, J. Differential Equations 252 (2012), no. 3, 2739-2758. crossref(new window)

9.
Y. Lei, C. Li, and C. Ma, Decay estimation for positive solutions of a ${\gamma}$-Laplace equation, Discrete Contin. Dyn. Syst. 30 (2011), no. 2, 547-558. crossref(new window)

10.
C. Li and L. Ma, Uniqueness of positive bound states to Schrodinger systems with critical exponents, SIAM J. Math. Anal. 40 (2008), no. 3, 1049-1057. crossref(new window)

11.
T. Lin and J. Wei, Ground state of N coupled nonlinear Schrodinger equations in ${\mathbb{R}}^n$, n $\leq$ 3, Commun. Math. Phys. 255 (2005), no. 3, 629-653. crossref(new window)

12.
P. Quittner and Ph. Souplet, Symmetry of components for semilinear elliptic systems, SIAM J. Math. Anal. 44 (2012), no. 4, 2545-2559. crossref(new window)

13.
J. Serrin and H. Zou, Cauchy-Liouville and universal boundedness theorems for quasilinear elliptic equations and inequalities, Acta Math. 189 (2002), no. 1, 79-142. crossref(new window)

14.
Ph. Souplet, The proof of the Lane-Emden conjecture in four space dimensions, Adv. Math. 221 (2009), no. 5, 1409-1427. crossref(new window)