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Counter-example for Liouville theorems for indefinite problems on half spaces

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Author(s): J. Foeldes

Journal: Acta Mathematica Universitatis Comenianae
ISSN 0862-9544

Volume: LXXXI;
Issue: 1;
Start page: 105;
Date: 2012;
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ABSTRACT
The goal of this paper is a construction of an counter-example to Liouville theorems for indefinite problems on half spaces. Since Liouville theorems are closely related to the scaling method for elliptic and parabolic problems, our counter-example indicates that one has to impose additional assumptions on the nodal set of nonlinearity in order to obtain a priori estimates for indefinite elliptic problems. The counter-example is constructed by shooting method in one-dimensional case and then extended to higher dimensions.
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