Constant mean curvature radial graphs over domains of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"> <mml:msup> <mml:mi mathvariant="double-struck">S</mml:mi> <mml:mi>n</mml:mi> </mml:msup> </mml:math>

We establish the existence of hypersurfaces with constant mean curvature and a prescribed boundary in Euclidean space, represented as radial graphs over domains of the unit sphere. Under the assumptions that the mean curvature of the domain’s boundary is positive and that a subsolution exists for the associated Dirichlet problem, we extend Serrin’s classical result to include the case of positive constant mean curvature.