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This paper is concerned about several quasilinear elliptic systems with $m$-Laplacians. According to the Liouville theorems of those systems on $\mathbb R^n$, we obtain the singularity estimates of the positive $C^1$-weak solutions on bounded or unbounded domain (but it is not $\mathbb R^n$) and their decay rates on the exterior domain when $|x| \to \infty$. The doubling lemma which is developed by Polacik-Quittner-Souplet plays a key role in this paper. In addition, the corresponding results of several special examples are presented.
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참고문헌 (24)
참고문헌 신청
M. -F. Bidaut-Veron / 2000 / Local behaviour of the solutions of a class of nonlinear elliptic systems / Adv. Differential Equations 5(1-3):147~192
M.-F. Bidaut-Veron / 1996 / Asymptotics of solutions of some nonlinear elliptic systems / Comm. Partial Differential Equations 21(7-8):1035~1086
J. Byeon / 2009 / Symmetry and monotonicity of least energy solutions / Calc. Var. Partial Differential Equations 36(4):481~492
P. Clement / 2000 / Existence of positive solutions for a nonvariational quasilinear elliptic system / J. Differential Equations 166(2):455~477
E. N. Dancer / 1998 / Superlinear problems on domains with holes of asymptotic shape and exterior problems / Math. Z 229(3):475~491
M.-F. Bidaut-Veron / 1996 / Asymptotics of solutions of some nonlinear elliptic systems / Comm. Partial Differential Equations 21(7-8):1035~1086
J. Byeon / 2009 / Symmetry and monotonicity of least energy solutions / Calc. Var. Partial Differential Equations 36(4):481~492
P. Clement / 2000 / Existence of positive solutions for a nonvariational quasilinear elliptic system / J. Differential Equations 166(2):455~477
E. N. Dancer / 1998 / Superlinear problems on domains with holes of asymptotic shape and exterior problems / Math. Z 229(3):475~491
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