, Volume 188, Issue 1, pp 155-179
Date: 09 Oct 2007

Non-existence of Entire Solutions of Degenerate Elliptic Inequalities with Weights

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Non-existence results for non-negative distribution entire solutions of singular quasilinear elliptic differential inequalities with weights are established. Such inequalities include the capillarity equation with varying gravitational field h, as well as the general p-Poisson equation of radiative cooling with varying heat conduction coefficient g and varying radiation coefficient h. Since we deal with inequalities and positive weights, it is not restrictive to assume h radially symmetric. Theorem 1 extends in several directions previous results and says that solely entire large solutions can exist, while Theorem 2 shows that in the p-Laplacian case positive entire solutions cannot exist. The results are based on some qualitative properties of independent interest.

Communicated by C. A. Stuart
An erratum to this article can be found at http://dx.doi.org/10.1007/s00205-007-0105-1