A NONLINEAR ULTRA-PARABOLIC DIFFERENTIAL INEQUALITY WITH BESSEL OPERATOR

In this paper, we investigate the existence and nonexistence of weak solutions to an ultra-parabolic differential inequality posed on the interval (0, 1), under an inhomogeneous Dirichlet boundary condition. The considered problem involves the singular Bessel operator d2 dx2 + alpha x d dx and a nonlinearity of the form x-6|u|p. Our approach is based on nonlinear capacity estimates and an appropriate choice of test functions.