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for indefinite problems on half spaces
Received: August 24, 2011; Accepted: December 21, 2011
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.
AMS Subject classification: Primary: 34B40, 34B15, 35B53, 35J25.
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