EIGENVALUE HOMOGENISATION PROBLEM WITH INDEFINITE WEIGHTS

A Krein Space Approach to Elliptic Eigenvalue Problems with Indefinite Weights

where L is a symmetric elliptic operator and r is a locally integrable function on Rn. If r is of constant sign then this problem leads to a selfadjoint problem in the Hilbert space L2(|r|). In this note we are interested in the case when r takes both positive and negative values on sets of positive measure. Then the spectrum of the problem (1) is not necessarily real any more. Moreover it is n...

Asymmetric Elliptic Problems with Indefinite Weights

– We prove the existence of a first nontrivial eigenvalue for an asymmetric elliptic problem with weights involving the laplacian (cf. (1.2) below) or more generally the p-laplacian (cf. (1.3) below). A first application is given to the description of the beginning of the Fučik spectrum with weights for these operators. Another application concerns the study of nonresonance for the problems (1....

On the Fučik Spectrum with Indefinite Weights

On the spectrum of a fourth order nonlinear eigenvalue problem with variable exponent and indefinite potential

The present paper deals with the spectrum of a fourth order nonlinear eigenvalue problem involving variable exponent conditions and a sign-changing potential. The main result of this paper establishes the existence of two positive constants λ0 and λ1 with λ0 ≤ λ1 such that every λ ∈ [λ1,+∞) is an eigenvalue, while λ ∈ (−∞, λ0) cannot be an eigenvalue of the above problem.

Principal eigenvalue for an elliptic problem with indefinite weight on cylindrical domains.

This paper is concerned with an indefinite weight linear eigenvalue problem in cylindrical domains. We investigate the minimization of the positive principal eigenvalue under the constraint that the weight is bounded by a positive and a negative constant and the total weight is a fixed negative constant. Biologically, this minimization problem is motivated by the question of determining the opt...