An eigenvalue problem for a quasilinear elliptic field equation on $\mathbb R^n$
Keywords
Nonlinear systems, nonlinear Schrödinger equations, nonlinear eigenvalue problemsAbstract
We study the field equation $$-\Delta u+V(x)u+\varepsilon^r(-\Delta_pu+W'(u))=\mu u$$ on $\mathbb R^n$, with $\varepsilon$ positive parameter. The function $W$ is singular in a point and so the configurations are characterized by a topological invariant: the topological charge. By a min-max method, for $\varepsilon$ sufficiently small, there exists a finite number of solutions $(\mu(\varepsilon),u(\varepsilon))$ of the eigenvalue problem for any given charge $q\in{\mathbb Z}\setminus\{0\}$.Downloads
Published
2001-06-01
How to Cite
1.
BENCI, Vieri, MICHELETTI, Anna Maria and VISETTI, Daniela. An eigenvalue problem for a quasilinear elliptic field equation on $\mathbb R^n$. Topological Methods in Nonlinear Analysis. Online. 1 June 2001. Vol. 17, no. 2, pp. 191 - 211. [Accessed 18 April 2024].
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