On non-negative solutions of quasilinear elliptic inequalities

:We study the solutions of the inequalities Lu greater than or equal to F(x, u), Lu. greater than or equal to F(x, u), where L=Sigma(i,j-1)(n) partial derivative/partial derivative x(i)[a(ij)(x)partial derivative/partial derivative x(j)], L = Sigma(i,j=1)(n) a(ij)(x)partial derivative(2)/partial derivative x(i)partial derivative x(j) are differential operators of elliptic type and F is some function.