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.
On the existence and the profile of nodal solutions of elliptic equations involving critical growth
MICHELETTI, ANNA MARIA;
2006-01-01
Abstract
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.File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
