Ghergu, MariusMariusGherguLiskevich, VitaliVitaliLiskevichSobol, ZeevZeevSobol2014-11-112015-07-242014-07-24Journal D'Analyse Mathematiquehttp://hdl.handle.net/10197/6149We study the existence and non-existence of positive singular solutions of second-order non-divergence type elliptic inequalities of the form $\sum\limits_{i,j = 1}^N {a_{ij} (x)\frac{{\partial ^2 u}} {{\partial x_i \partial x_j }}} + \sum\limits_{i = 1}^N {b_i (x)\frac{{\partial u}} {{\partial x_i }} \geqslant K(x)u^p ,} - \infty < p - \infty , $ with measurable coefficients in a punctured ball B R \{0} of ℝ N , N ≥ 1. We prove the existence of a critical value p* which separates the existence region from the non-existence region. We show that in the critical case p = p*, the existence of a singular solution depends on the rate at which the coefficients (a i j ) and (b i ) stabilize at zero, and we provide some optimal conditions in this setting.enThe final publication is available at www.springerlink.comNon-divergence semi-linear equationSingular solutionsPunctured ballCritical exponentJournal Article123125127910.1007/s11854-014-0020-y2014-11-07https://creativecommons.org/licenses/by-nc-nd/3.0/ie/