Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 1040.35026
Garc\'ia-Melián, Jorge
A remark on the existence of large solutions via sub and supersolutions. (English)
[J] Electron. J. Differ. Equ. 2003, Paper No. 110, 4 p., electronic only (2003). ISSN 1072-6691/e

The author considers the boundary blow-up elliptic problem $$\cases \Delta u= a(x)f(u)\quad &\text{in }\Omega,\\ u=+\infty\quad &\text{on }\partial\Omega,\endcases\tag1$$ where $\Omega\subset\bbfR^N$, $N\ge 2$ is a smooth bounded domain, $a(x)$ is a Hölder continuous positive function defined in $\Omega$ and $f$ is locally Hölder in $(0,+\infty)$. The author is mainly interested in the existence of positive classical solutions to (1), that is solutions $u\in C^2(\Omega)$ to $\Delta u= a(x)f(u)$ such that $u(x)\to +\infty$ as $d(x):= \text{dist}(x,\partial\Omega)\to 0$. Using sub- and supersolution techniques the author proves the existence of at least one positive solution under some suitable assumptions on $a$ and $f$.
[Messoud A. Efendiev (Berlin)]

MSC 2000:: *35J60 Nonlinear elliptic equations
35J25 Second order elliptic equations, boundary value problems

Keywords: boundary blow-up; sup- and supersolutions

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]