Archive for Rational Mechanics and Analysis

, Volume 188, Issue 1, pp 155–179

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


    • Dipartimento di Matematica e InformaticaUniversità degli Studi di Perugia
  • Patrizia Pucci
    • Dipartimento di Matematica e InformaticaUniversità degli Studi di Perugia
  • Marco Rigoli
    • Dipartimento di MatematicaUniversità degli Studi di Milano

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

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.

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© Springer-Verlag 2007