Abstract/Details

## Maximum principle methods for semilinear elliptic problems

Shaker, Aihua Wang.   University of Connecticut ProQuest Dissertations Publishing,  1990. 9102036.

### Abstract (summary)

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) $\int\sbsp{1}{\infty} t\sp{n-1+\gamma(n-2)}\phi(t)dt < \infty$.

### Indexing (details)

Subject
Mathematics
Classification
0405: Mathematics
Identifier / keyword
Pure sciences; symmetry
Title
Maximum principle methods for semilinear elliptic problems
Author
Shaker, Aihua Wang
Number of pages
65
Degree date
1990
School code
0056
Source
DAI-B 51/08, Dissertation Abstracts International
Place of publication
Ann Arbor
Country of publication
United States
ISBN
979-8-206-89869-9
McKenna, Patrick J.
University/institution
University of Connecticut
University location
United States -- Connecticut
Degree
Ph.D.
Source type
Dissertation or Thesis
Language
English
Document type
Dissertation/Thesis
Dissertation/thesis number
9102036
ProQuest document ID
303846596