We study the existence of nodal solutions to the boundary value problem − Δ u = |u|p − 1u in a bounded, smooth domain Ω in ℝ2, with homogeneous Dirichlet boundary condition, when p is a large exponent. We prove that, for p large enough, there exist at least two pairs of solutions which change sign exactly once and whose nodal lines intersect the boundary of Ω.
On the existence and profile of nodal solutions for a two-dimensional elliptic problem with large exponent in nonlinearity / Esposito, P; Musso, M; Pistoia, Angela. - In: PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY. - ISSN 0024-6115. - STAMPA. - 3:(2007), pp. 497-519. [10.1112/plms/pdl020]
On the existence and profile of nodal solutions for a two-dimensional elliptic problem with large exponent in nonlinearity
PISTOIA, Angela
2007
Abstract
We study the existence of nodal solutions to the boundary value problem − Δ u = |u|p − 1u in a bounded, smooth domain Ω in ℝ2, with homogeneous Dirichlet boundary condition, when p is a large exponent. We prove that, for p large enough, there exist at least two pairs of solutions which change sign exactly once and whose nodal lines intersect the boundary of Ω.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
