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arXiv · 1611.06719

Existence of bounded variation solutions for a $1-$Laplacian problem with vanishing potentials

G. M. Figueiredo·M. T. O. Pimenta
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Abstract

In this work it is studied a quasilinear elliptic problem in the whole space $\mathbb{R}^N$ involving the $1-$Laplacian operator, with potentials which can vanish at infinity. The Euler-Lagrange functional is defined in a space whose definition resembles $BV(\mathbb{R}^N)$ and, in order to avoid working with extensions of it to some Lebesgue space, we state and prove a version of the Mountain Pass Theorem without the Palais-Smale condition to Lipschitz continuous functionals.

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G. M. Figueiredo, M. T. O. Pimenta. 2016-11-21. Existence of bounded variation solutions for a $1-$Laplacian problem with vanishing potentials. https://arxiv.org/abs/1611.06719

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