Electron.n. J. Diff. Eqns., Vol. 1999(1999), No. 22, pp. 1-15.
### Antimaximum principle for elliptic problems with weight

T. Godoy, J.-P. Gossez, & S. Paczka

**Abstract:**

This paper is concerned with the antimaximum principle for the linear
problem with weight

under Dirichlet or Neumann boundary conditions.
We investigate the following three questions:

Where exactly can this principle hold?

If it holds, does it hold uniformly or not?

If it holds uniformly, what is the exact interval of uniformity?

We will in particular obtain a variational characterization of
this interval of uniformity.
Submitted February 2, 1999. Published June 17, 1999.

Math Subject Classification: 35J20, 35P05.

Key Words: Antimaximum principle, indefinite weight, Fucik spectrum.

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T. Godoy

FAMAF, Univ. Nacional Cordoba

Ciudad universitaria, 5000 Cordoba, Argentina

e-mail: godoy@mate.uncor.edu
J.-P. Gossez

Dep. Mathematique, C.P. 214

Universite Libre de Bruxelles

1050 Bruxelles, Belgique

e-mail: gossez@ulb.ac.be

S. Paczka

FAMAF, Univ. Nacional Cordoba

Ciudad universitaria, 5000 Cordoba, Argentina

e-mail: paczka@mate.uncor.edu

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