Eigenvalue problems for indefinite-weight linear elliptic equations in ℝN
(EN)
Stavrakakis, NM
(EN)
In this paper we are going to discuss the existence of positive eigenvalues of a linear polyharmonic equation on all of R(N). A weight function g is an element of L(N/2m)(R(N)) is present in the equation, which changes sign on R(N). The eigenfunction. space is characterised in terms of the ''energy norm'' as well as an equivalent ''weighted norm''. First, the positivity, the regularity, the decay at infinity, and the simplicity of the associated eigenfunctions are discussed, for the Laplace.
(EN)
