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A Kirchhoff‐type equation involving critical exponent and sign‐changing weight functions in dimension four
Author(s) -
Lou QingJun
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5061
Subject(s) - mathematics , multiplicity (mathematics) , mathematical analysis , regular polygon , compact space , exponent , dimension (graph theory) , critical exponent , pure mathematics , geometry , scaling , philosophy , linguistics
In the paper, we study the existence and multiplicity of positive solutions for the following Kirchhoff equation involving concave‐convex nonlinearities: 1− a ∫ Ω∇ u2 d x + b Δ u = λ g ( x )uq − 2 u + h ( x )up − 2 u in Ω ,u ∈ H 0 1 ( Ω ) .We obtain the existence and multiplicity of solutions of [Disp. Item 1. 1 −a∫Ω∇u2dx+bΔu=λg(x)uq−2u+h(x)up−2uinΩ,u∈H01(Ω), ...] by variational methods and concentration compactness principle.