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Asymptotic behavior of solutions of elliptic equations II: Analogues of liouville’s theorem for solutions of inequalities onRn,n≧3

✍ Scribed by Leon Karp

Book ID
112897010
Publisher
Springer-Verlag
Year
1981
Tongue
English
Weight
445 KB
Volume
39
Category
Article
ISSN
0021-7670

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The elliptic equation \(\Delta u+f(u)=0\) in \(R^{n}\) is discussed in the case where \(f(u)=\) \(|u|^{n} \quad u(|u| \geqslant 1),=|u|^{4} \quad{ }^{1} u(|u|<1), 10\). It is further proved that for any \(k \geqslant 0\) there exist at least three radially symmetric solutions which have exactly \(k\