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

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DOI: 10.1007/s00205-007-0081-5

- Cite this article as:
- Filippucci, R., Pucci, P. & Rigoli, M. Arch Rational Mech Anal (2008) 188: 155. doi:10.1007/s00205-007-0081-5

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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.