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Solutions with prescribed number of nodes to superlinear elliptic systems

✍ Scribed by Daomin Cao; Zhongwei Tang

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
246 KB
Volume
55
Category
Article
ISSN
0362-546X

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✦ Synopsis

We consider a class of elliptic systems in the following form:

We prove the existence of inΓΏnitely many solutions which are characterized by the number of nodes of each component. Our argument is based upon an extension of the results of Terracini and Verzini (Nonlinear Di erential Equations Appl. 8 (2001) 323).

πŸ“œ SIMILAR VOLUMES

Radial Solutions of Semilinear Elliptic
Radial Solutions of Semilinear Elliptic Equations with Prescribed Numbers of Zeros
✍ S. Maier πŸ“‚ Article πŸ“… 1994 πŸ› Elsevier Science 🌐 English βš– 989 KB

We study solutions \(u=u(t)\) of an initial value problem for \(u^{\prime \prime}+((n-1) / t) u^{\prime}+\) \(f(u)=0\). Under certain conditions on the nonlinearity \(f\) (for instance \(f(u)=\) \(\left.-|u|^{q}+|u|^{\hat{q}-1} u, 12\right)\), we get the existence of some initial values, such that t