Entire large solutions for semilinear elliptic equations
Entire large solutions for semilinear elliptic equations
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DOI：
10.1016/j.jde.2012.05.024
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发表时间：
2011-11
影响因子：
2.4
通讯作者：
L. Dupaigne;M. Ghergu;O. Goubet;G. Warnault
中科院分区：
文献类型：
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作者：
L. Dupaigne;M. Ghergu;O. Goubet;G. Warnault
我们分析半线性椭圆方程Δu=ρ(x)f(u), u>0在RD（D大于或等于3）中，特别强调整个大解决方案的定性研究，即解决方案u使得lim|x|→+∞u(x)=+∞。假设f满足Keller-Osserman增长假设，并且ρ在适当意义上在无穷大处衰减，我们证明了整个大解的存在性。然后讨论了解的渐近性、唯一性和对称性等较为精细的问题。
We analyze the semilinear elliptic equation Δu=ρ(x)f(u), u>0 in RD(D⩾3), with a particular emphasis put on the qualitative study of entire large solutions, that is, solutions u such that lim|x|→+∞u(x)=+∞. Assuming that f satisfies the Keller–Osserman growth assumption and that ρ decays at infinity in a suitable sense, we prove the existence of entire large solutions. We then discuss the more delicate questions of asymptotic behavior at infinity, uniqueness and symmetry of solutions.