Topological Methods in Nonlinear Analysis

An eigenvalue problem for a quasilinear elliptic field equation on $\mathbb R^n$

V. Benci, A. M. Micheletti, and D. Visetti

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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 $q\in{\mathbb Z}\setminus\{0\}$.

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Topol. Methods Nonlinear Anal., Volume 17, Number 2 (2001), 191-211.

First available in Project Euclid: 22 August 2016

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Benci, V.; Micheletti, A. M.; Visetti, D. An eigenvalue problem for a quasilinear elliptic field equation on $\mathbb R^n$. Topol. Methods Nonlinear Anal. 17 (2001), no. 2, 191--211.

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