A note on exponential decay properties of ground states for quasilinear elliptic equations. (English) Zbl 1102.35038

Li, Yi; Zhao, Chunshan

Proc. Am. Math. Soc. 133, No. 7, 2005-2012 (2005).

The authors give an explicit formula for exponential decay properties of ground states for a class of quasilinear elliptic equations in the whole space \(\mathbb R^N\).

Reviewer: Lubomira Softova (Bari)

MSC:

35J60	Nonlinear elliptic equations
35B45	A priori estimates in context of PDEs
35J70	Degenerate elliptic equations

Keywords:

m-Laplace operator; ground states; exponential decay

References:

[1]	Shmuel Agmon, Lectures on exponential decay of solutions of second-order elliptic equations: bounds on eigenfunctions of \?-body Schrödinger operators, Mathematical Notes, vol. 29, Princeton University Press, Princeton, NJ; University of Tokyo Press, Tokyo, 1982. · Zbl 0503.35001
[2]	B. Gidas, Wei Ming Ni, and L. Nirenberg, Symmetry of positive solutions of nonlinear elliptic equations in \?\(^{n}\), Mathematical analysis and applications, Part A, Adv. in Math. Suppl. Stud., vol. 7, Academic Press, New York-London, 1981, pp. 369 – 402. · Zbl 0469.35052
[3]	Yi Li, Asymptotic behavior of positive solutions of equation \Delta \?+\?(\?)\?^{\?}=0 in \?\(^{n}\), J. Differential Equations 95 (1992), no. 2, 304 – 330. · Zbl 0778.35010
[4]	Wei-Ming Ni and Izumi Takagi, On the shape of least-energy solutions to a semilinear Neumann problem, Comm. Pure Appl. Math. 44 (1991), no. 7, 819 – 851. · Zbl 0754.35042
[5]	Wei-Ming Ni and Juncheng Wei, On the location and profile of spike-layer solutions to singularly perturbed semilinear Dirichlet problems, Comm. Pure Appl. Math. 48 (1995), no. 7, 731 – 768. · Zbl 0838.35009
[6]	James Serrin and Moxun Tang, Uniqueness of ground states for quasilinear elliptic equations, Indiana Univ. Math. J. 49 (2000), no. 3, 897 – 923. · Zbl 0979.35049