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Antimaximum principle for elliptic problems with weight. (English) Zbl 0920.35045
Summary: This paper is concerned with the antimaximum principle for the linear problem with weight \(-\Delta u=\lambda m(x)u+ h(x)\), 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.

35J20 Variational methods for second-order elliptic equations
35B50 Maximum principles in context of PDEs
35P05 General topics in linear spectral theory for PDEs
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