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Sign‐changing solutions for a nonhomogeneous Paneitz‐type problem
Author(s) -
Alarcón Salomón,
Varela Nicolás
Publication year - 2020
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201800186
Subject(s) - mathematics , sign (mathematics) , bounded function , homogeneous space , domain (mathematical analysis) , polygon (computer graphics) , type (biology) , pure mathematics , regular polygon , degree (music) , construct (python library) , reduction (mathematics) , mathematical analysis , geometry , computer science , telecommunications , ecology , physics , frame (networking) , acoustics , biology , programming language
We consider the problemP εΔ 2 u = | u | 8 N − 4u + ε f ( x )in Ω , u = Δ u = 0on ∂ Ω , where Ω is a bounded smooth domain in R N , N ≥ 5 , that exhibits certain symmetries and contains the origin, f ∈ L ∞ ( Ω ) , f ≥ 0 , f ≢ 0 , and ε > 0 is a small parameter. By using the Lyapunov–Schmidt reduction method and topological degree theory, for each sufficiently large k ∈ N , we construct sign‐changing solutions to ( P ε ) exhibiting k negative spikes at the vertices of a regular polygon and a single positive spike at the origin.