We show that the problem at critical growth, involving the $1$-Laplace operator and obtained by relaxation of $-\Delta_1 u=\lambda |u|^{-1}u+|u|^{1^*-2}\,u$, admits a nontrivial solution $u\in BV(\Omega)$ for any $\lambda\geq\lambda_1$. Nonstandard linking structures, for the associated functional, are recognized.

Degiovanni, M., Magrone, P. (2009). Linking solutions for quasilinear equations at critical growth involving the $1$-Laplace. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 36, 591-609 [10.1007/s00526-009-0246-1].

### Linking solutions for quasilinear equations at critical growth involving the $1$-Laplace

#### Abstract

We show that the problem at critical growth, involving the $1$-Laplace operator and obtained by relaxation of $-\Delta_1 u=\lambda |u|^{-1}u+|u|^{1^*-2}\,u$, admits a nontrivial solution $u\in BV(\Omega)$ for any $\lambda\geq\lambda_1$. Nonstandard linking structures, for the associated functional, are recognized.
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Degiovanni, M., Magrone, P. (2009). Linking solutions for quasilinear equations at critical growth involving the $1$-Laplace. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 36, 591-609 [10.1007/s00526-009-0246-1].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11590/142519
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