Existence of bounded variation solutions for a $1-$Laplacian problem with vanishing potentials
| Autor: | Figueiredo, G. M., Pimenta, M. T. O. |
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| Rok vydání: | 2016 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 26 pages. arXiv admin note: substantial text overlap with arXiv:1610.07369 |
| Databáze: | arXiv |
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