Please use this identifier to cite or link to this item: http://hdl.handle.net/10077/4270
 Title: On global solutions to a semilinear elliptic boundary problem in an unbounded domain Authors: Egorov, Yuri V.Kondratiev, Vladimir A. Issue Date: 2000 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. Series/Report no.: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics31 (2000) suppl.2 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 $\left\{ x=\left(x',x_{n}\right)\::\:\mid x'\mid$ in $\mathbf{R}^{n}$. We study the asymptotic behiaviour as $x_{n}\rightarrow\infty$of the solutions of $\left(1\right)$ satisfying the nonlinear boundarycondition $\frac{\partial u}{\partial N}-b\left(x\right)\mid u\left(x\right)\mid^{p-1}u\left(x\right)=0\qquad\qquad\left(2\right)$ on the lateral surface $S=\left\{ x\epsilon\partial Q,\;0$ where p>0, b(x)$\geq b_{0}$ >0. We show that a global solution ofthe problem can exist not for all values of parameters p, $\sigma$and indicate these values. The boundary problem in the cylinder wasstudied by us in $\left[1\right]$,$\left[2\right]$. The obtainedresults generalize some results of B. Hu in $\left[4\right]$. Type: Article URI: http://hdl.handle.net/10077/4270 ISSN: 0049-4704 Appears in Collections: Rendiconti dell'Istituto di Matematica dell'Università di Trieste: an International Journal of Mathematics vol.31 (2000) s2

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