Asymptotic behavior of positive solutions of some quasilinear elliptic problems

Zongming Guo and Li Ma

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Asymptotic behavior of positive solutions of some quasilinear elliptic problems

机译：一类拟线性椭圆问题正解的渐近性。

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We discuss the asymptotic behavior of positive solutions of the quasilinear elliptic problem ?Δ_pu = a up?1?b(x) uq, u|_{? Ω} = 0, as q → p ? 1 + 0 and as q → ∞, via a scale argument. Here Δ_p is the p-Laplacian with 1 < p ∞ and q > p ? 1. If p = 2, such problems arise in population dynamics. Our main results generalize the results for p = 2, but some technical difficulties arising from the nonlinear degenerate operator ?Δ_p are successfully overcome. As a by-product, we can solve a free boundary problem for a nonlinear p-Laplacian equation.

机译：我们讨论了拟线性椭圆问题？Δ_{p u = au p？1 ？b（x）u q 的正解的渐近行为，u | _{？ Ω = 0，因为q→p？ 1 + 0且通过比例参数为q→∞。这里的Δ_{p 是1 ∞和q> p？的p-Laplacian。 1.如果p = 2，则人口动态会出现此类问题。我们的主要结果推广了p = 2的结果，但是成功克服了非线性简并算子？Δ_{p 引起的一些技术难题。作为副产品，我们可以解决非线性p-Laplacian方程的自由边界问题。}}}}

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《Journal of the London Mathematical Society》 |2007年第2期|419-437|共19页
作者
Zongming Guo and Li Ma;
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Department of MathematicsDong Hua UniversityShanghai 200051P.R. Chinaguozm{at}public.xxptt.ha.cn Department of Mathematical SciencesTsinghua UniversityBeijing 100084P.R. China;

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1. ASYMPTOTIC BEHAVIOR OF POSITIVE SOLUTIONS FOR A CLASS OF QUASILINEAR ELLIPTIC EQUATIONS WITH GENERAL NONLINEARITIES [J] . Shinji Adachi, Masataka Shibata, Tatsuya Watanabe Communications on pure and applied analysis . 2014,第1期

机译：一类具有一般非线性拟线性椭圆型方程正解的渐近性。
2. Existence and asymptotic behavior of positive solution to a quasilinear elliptic problem in R-N [J] . Covei DP Nonlinear Analysis: An International Multidisciplinary Journal . 2008,第8期

机译：R-N中一个拟线性椭圆问题正解的存在性与渐近性
3. Asymptotic behavior of positive solutions of some quasilinear elliptic problems [J] . Guo ZM, Ma L The Journal of the London Mathematical Society . 2007,第2期

机译：一类拟线性椭圆问题正解的渐近性。
4. Multiple existence of positive solutions to quasilinear elliptic equations involving indefinite lower terms [C] . Kimiaki Narukawa International Conference on Mathematical Problems in Engineering, Aerospace and Sciences . 2012

机译：拟线性椭圆方程的阳性解的多重存在涉及无限期术语
5. On the existence of positive solutions of quasilinear elliptic boundary value problems. [D] . Kim, Eun Heui. 1999

机译：关于拟线性椭圆边值问题的正解的存在性。
6. Multiple Solutions for a Class of Dirichlet Double Eigenvalue Quasilinear Elliptic Systems Involving the (p1… pn)-Laplacian Operator [O] . Armin Hadjian, Saleh Shakeri 2013

机译：一类Dirichlet双特征值拟线性椭圆系统的多重解其中（p1…pn）-拉普拉斯算子
7. ASYMPTOTIC BEHAVIOR OF POSITIVE SOLUTIONS FOR A CLASS OF QUASILINEAR ELLIPTIC EQUATIONS WITH GENERAL NONLINEARITIES [O] . Shinji Adachi, Masataka Shibata, Tatsuya Watanabe 2014

机译：一类具有一般非线性拟线性椭圆型方程正解的渐近性。
8. Asymptotic Behavior of Solutions to the Damped Quasilinear Equation [R] . Bloom, F. 1981

机译：阻尼拟线性方程解的渐近性

Asymptotic behavior of positive solutions of some quasilinear elliptic problems

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