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On the existence and profile of nodal solutions for a two‐dimensional elliptic problem with large exponent in nonlinearity
Author(s) -
Esposito Pierpaolo,
Musso Monica,
Pistoia Angela
Publication year - 2007
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/pdl020
Subject(s) - mathematics , exponent , bounded function , mathematical analysis , boundary value problem , nonlinear system , dirichlet boundary condition , domain (mathematical analysis) , nodal , boundary (topology) , sign (mathematics) , homogeneous , critical exponent , pure mathematics , geometry , combinatorics , physics , scaling , medicine , philosophy , linguistics , quantum mechanics , anatomy
We study the existence of nodal solutions to the boundary value problem − Δ u = | u | p − 1 u in a bounded, smooth domain Ω in ℝ 2 , 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.