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

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.
Bartsch, T; Micheletti, ANNA MARIA; Pistoia, A.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11568/100861
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