Search results for " eigenvalues"
showing 4 items of 14 documents
Some applications of the Chambers isoperimetric inequality
2022
In this paper, using the Chambers isoperimetric inequality, we introduce the notion of weighted rearrangement of a function associated to the measure $f dx$, where $f(x)=e^{g(|x|)}$ for $x \in \mathbb{R}^n}$, with $g$ smooth, convex and even. Then we give some of its applications to variational inequalities and PDEs via weighted symmetrization.
A sharp estimate for Neumann eigenvalues of the Laplace-Beltrami operator for domains in a hemisphere
2018
Here, we prove an isoperimetric inequality for the harmonic mean of the first [Formula: see text] non-trivial Neumann eigenvalues of the Laplace–Beltrami operator for domains contained in a hemisphere of [Formula: see text].
(p,2)-equations resonant at any variational eigenvalue
2018
We consider nonlinear elliptic Dirichlet problems driven by the sum of a p-Laplacian and a Laplacian (a (p,2) -equation). The reaction term at ±∞ is resonant with respect to any variational eigenvalue of the p-Laplacian. We prove two multiplicity theorems for such equations.
Multiplicity of solutions for asymptotically linear $n$-th order boundary value problems
2007
In this paper we investigate existence and multiplicity of solutions, with prescribed nodal properties, to a two-point boundary value problem of asymptotically linear $n$-th order equations. The proof follows a shooting approach and it is based on the weighted eigenvalue theory for linear $n$-th order boundary value problems