This work is devoted to the Dirichlet problem for the equation -δ u = λu +|x|α|u|2*-2 u in the unit ball of ℝN. We assume that λ is bigger than the first eigenvalues of the laplacian, and we prove that there exists a solution provided a is small enough. This solution has a variational characterization as a ground state.
Secchi, S. (2012). The Brezis-Nirenberg Problem for the Henon Equation: Ground State Solutions. ADVANCED NONLINEAR STUDIES, 12(2), 383-394 [10.1515/ans-2012-0209].
The Brezis-Nirenberg Problem for the Henon Equation: Ground State Solutions
Secchi, S
2012
Abstract
This work is devoted to the Dirichlet problem for the equation -δ u = λu +|x|α|u|2*-2 u in the unit ball of ℝN. We assume that λ is bigger than the first eigenvalues of the laplacian, and we prove that there exists a solution provided a is small enough. This solution has a variational characterization as a ground state.
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