The least eigenvalues of nonhomogeneous degenerated quasilinear eigenvalue problems

A note on quasilinear elliptic eigenvalue problems

We study an eigenvalue problem by a non-smooth critical point theory. Under general assumptions, we prove the existence of at least one solution as a minimum of a constrained energy functional. We apply some results on critical point theory with symmetry to provide a multiplicity result.

Nonlinear Eigenvalue Problems with Specified Eigenvalues

This work considers eigenvalue problems that are nonlinear in the eigenvalue parameter. Given such a nonlinear eigenvalue problem T , we are concerned with finding the minimal backward error such that T has a set of prescribed eigenvalues with prescribed algebraic multiplicities. While the usual resolvent norm addresses this question for a single eigenvalue of multiplicity one, the general sett...

Generalized Eigenvalue Problems with Specified Eigenvalues

We consider the distance from a (square or rectangular) matrix pencil to the nearest matrix pencil in 2-norm that has a set of specified eigenvalues. We derive a singular value optimization characterization for this problem and illustrate its usefulness for two applications. First, the characterization yields a singular value formula for determining the nearest pencil whose eigenvalues lie in a...

Quasilinear Elliptic Systems of Resonant Type and Nonlinear Eigenvalue Problems

An inequality for eigenvalues of quasilinear problems with monotonic weights

In this work we extend an inequality of Nehari to the eigenvalues of weighted quasilinear problems involving the p-laplacian when the weight is a monotonic function. We apply it to different eigenvalue problems.