Asymptotic behaviour of positive solutions of semilinear elliptic problems with increasing powers
Keyword(s):
We prove existence results of two solutions of the problem \[ \begin{cases} L(u)+u^{m-1}=\lambda u^{p-1} & \text{in}\ \Omega,\\ u>0 & \text{in}\ \Omega,\\ u=0 & \text{on}\ \partial \Omega, \end{cases} \] where $L(v)=-\textrm {div}(M(x)\nabla v)$ is a linear operator, $p\in (2,2^{*}]$ and $\lambda$ and $m$ sufficiently large. Then their asymptotical limit as $m\to +\infty$ is investigated showing different behaviours.
1982 ◽
Vol 93
(1-2)
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pp. 1-14
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1987 ◽
Vol 39
(5)
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pp. 1162-1173
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2007 ◽
Vol 24
(1)
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pp. 41-60
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2007 ◽
Vol 240
(1)
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pp. 58-91
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1996 ◽
Vol 26
(8)
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pp. 1323-1346
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1981 ◽
Vol 12
(1)
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pp. 9-19
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1985 ◽
Vol 57
(3)
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pp. 349-372
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1993 ◽
Vol 18
(7-8)
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pp. 1219-1229
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Keyword(s):
1991 ◽
Vol 113
(2)
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pp. 415-415
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