  We prove the existence of p-harmonic functions under the form u(r, $\sigma$)
= r --$\beta$ $\omega$($\sigma$) in any cone C S generated by a spherical
domain S and vanishing on $\partial$C S. We prove the uniqueness of the
exponent $\beta$ and of the normalized function $\omega$ under a Lipschitz
condition on S.
