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Abstract/Details
Equations of the form $\Delta u+f(u)=0$ have been extensively studied in a bounded domain $\Omega$ of $R\sp N$, especially in finding steady states of reaction diffusion systems. In this paper, we extend the symmetry result given by Gidas, Ni, and Nirenberg to certain types of systems.
We also study the singular equation $\Delta u+p(x)u\sp{-\gamma}=0$ in $R\sp{n}$. We show that the above equation has a bounded, positive, $C\sp{2+\alpha}$ entire solution $u(x)$ vanishing at $\infty$ at the rate of at least $r\sp{q(2-n)}$, $0 < q < 1$, if $p(x)$ satisfies the following conditions: (1) $p(x) \in C\sbsp{loc}{\alpha} (R\sp n), n \geq 3, p(x) > 0, x \in R\sp n\\\{0\}$; (2) there exists $C > 0$, such that $C\phi(\vert x\vert) \leq \phi(\vert x\vert), \phi(x) = max\sb{\vert x\vert=t}p(x)$, $0 \leq t \leq \infty$; (3) $\int\sbsp{1}{\infty} t\sp{n-1+\gamma(n-2)}\phi(t)dt < \infty$.
Classification
0405: Mathematics
Identifier / keyword
Pure sciences; symmetry
Title
Maximum principle methods for semilinear elliptic problems
Author
Shaker, Aihua Wang
Source
DAI-B 51/08, Dissertation Abstracts International
Advisor
McKenna, Patrick J.
University/institution
University of Connecticut
University location
United States -- Connecticut
Source type
Dissertation or Thesis
Document type
Dissertation/Thesis
Dissertation/thesis number
9102036
ProQuest document ID
303846596
Copyright
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.
Document URL
https://www.proquest.com/docview/303846596/abstract