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
Magrone Paola
2009-01-01
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.File in questo prodotto:
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