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On global solutions to a semilinear elliptic boundary problem in an unbounded domain
Egorov, Yuri V.
Kondratiev, Vladimir A.
2000
Abstract
We consider solutions to the elliptic linear equation
\[
Lu:=\underset{i,j=1}{\overset{n}{\sum}}\frac{\partial}{\partial x_{i}}\left(a_{ij}\left(x\right)\frac{\partial u}{\partial x_{j}}\right)=0\qquad\qquad\left(1\right)
\]
of second order in an unbounded domain
\[
\left\{ x=\left(x',x_{n}\right)\::\:\mid x'\mid0, b(x)$\geq b_{0}$ >0. We show that a global solution of
the problem can exist not for all values of parameters p, $\sigma$
and indicate these values. The boundary problem in the cylinder was
studied by us in $\left[1\right]$,$\left[2\right]$. The obtained
results generalize some results of B. Hu in $\left[4\right]$.
Series
Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics
31 (2000) suppl.2
Publisher
Università degli Studi di Trieste. Dipartimento di Scienze Matematiche
Source
Yury V. Egorov and Vladimir A. Kondratiev, "On global solutions to a semilinear elliptic boundary problem in an unbounded domain", in: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics, 31 (2000) suppl.2, pp. 87-102.
Languages
en
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