Existence and nonexistence of solutions for the mean curvature equation with weights (Q6634477)

This study investigates the presence and absence of positive radial solutions for a Dirichlet problem involving the prescribed mean curvature operator with weighted terms in a ball of an appropriate radius. The inclusion of diverse weights, which may be singular or degenerate, introduces significant complexity to the problem, necessitating a detailed qualitative examination of the solutions. The analysis leverages Liouville-type results derived from a specialized Pohozaev identity. Furthermore, the authors provide sufficient criteria under which global solutions exhibit oscillatory behavior.