On the existence and the profile of nodal solutions of elliptic equations involving critical growth

We study the existence of sign changing solutions to the slightly subcritical problem −\Delta u = |u|^{p−1−ε}u in ω, u = 0 on ∂ω, on where ω is a smooth bounded domain in ℝ^N , N ≥ 3, p = (N + 2)/(N − 2) and ɛ > 0. We prove that, for ɛ small enough, there exist N pairs of solutions which change sign exactly once. Moreover, the nodal surface of these solutions intersects the boundary of ω, provided some suitable conditions are satisfied.