In this paper we will discuss three different problems which share the same conclusions. In the first one we revisit the well known Faber–Krahn inequality for the principal eigenvalue of the p-Laplace operator with zero homogeneous Dirichlet boundary conditions. Motivated by Chatelain, Choulli, and Henrot, 1996, we show in case the equality holds in the… (More)
In this note we use the Nehari manifold and fibering maps to show existence of positive solutions for a nonlinear biharmonic equation in a bounded smooth domain in R n , when n = 5, 6, 7.
In this note we introduce a variational problem with respect to an integrable fuzzy set f. The energy functional is maximized over a deleted σ-algebra. Using the decreasing rearrangement of f we prove that the admissible set can be replaced by the more convenient set of cuts of f. Finally an special case is considered where the variational problem can be… (More)
This note extends the results in , by describing the dependence of the optimal constant in the p-version of Friedrichs' inequality on the boundary integral term. In particular, it is shown that this constant is continuous, increasing, concave and increases to the optimal constant for the Dirichlet problem as s → ∞.