We analyse symmetry breaking for ground states of the Hénon equation [7] in a ball. Asymptotic estimates of the transition are also given when p is close to either 2 or 2 * .

We prove embedding results of weighted W 1,p (R N ) spaces of radially symmetric functions. The results then are used to obtain ground and bound state solutions of quasilinear equations with unbounded or decaying radial potentials.

Abstract. We establish some embedding results of weighted Sobolev spaces of radially symmetric functions. The results then are used to obtain ground state solutions of nonlinear Schrödinger equations with unbounded and decaying radial potentials. Our work unifies and generalizes many existing partial results in the literature.

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We study weighted Sobolev type embeddings of radially symmetric functions from W 1,p r (R N ; V) into L q (R N ; Q) for q < p with singular potentials. We then investigate the existence of nontrivial radial solutions of quasilinear elliptic equations with singular potentials and sub-p-linear nonlinearity. The model equation is of the form −div(|∇u| p−2 ∇u) + V (|x|)|u| p−2 u = Q(|x|)|u| q−2 u, x ∈ R N , u(x) → 0, |x| → ∞.