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.
Non-existence of Entire Solutions of Degenerate Elliptic Inequalities with Weights / R. Filippucci, P. Pucci, M. Rigoli. - In: ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS. - ISSN 0003-9527. - 188:1(2008), pp. 155-179.
Non-existence of Entire Solutions of Degenerate Elliptic Inequalities with Weights
M. RigoliUltimo
2008
Abstract
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.Pubblicazioni consigliate
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