An eigenvalue problem for a quasilinear elliptic field equation on $\mathbb R^n$
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Nonlinear systems, nonlinear Schrödinger equations, nonlinear eigenvalue problemsAbstrakt
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 $q\in{\mathbb Z}\setminus\{0\}$.Pobrania
Opublikowane
2001-06-01
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1.
BENCI, Vieri, MICHELETTI, Anna Maria & VISETTI, Daniela. An eigenvalue problem for a quasilinear elliptic field equation on $\mathbb R^n$. Topological Methods in Nonlinear Analysis [online]. 1 czerwiec 2001, T. 17, nr 2, s. 191–211. [udostępniono 3.7.2024].
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