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., Linking solutions for quasilinear equations at critical growth involving the "1-Laplace" operator, <<CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS>>, 2009; 36 (4): 591-609. [doi:10.1007/s00526-009-0246-1] [http://hdl.handle.net/10807/3312]
Linking solutions for quasilinear equations at critical growth involving the "1-Laplace" operator
Degiovanni, Marco;
2009
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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