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Solvability Of The P(x)-Kirchhoff Problem With Singular Terms

Posted on:2022-11-29Degree:MasterType:Thesis
Country:ChinaCandidate:Y X XiaoFull Text:PDF
GTID:2510306779478594Subject:Master of Engineering
Abstract/Summary:
In this paper,we study the existence of multiple solutions for a class of p(x)Kirchhoff type questions involving singular terms.By using the Nehari manifold,Ekeland’s variational principle and systemtric mountain pass theorem and other variational methods.Firstly,we consider the following p(x)-Kirchhoff type equations with singular nonlinear terms where Ω(?)RN(N≥3)is a smooth bounded domain with boundary (?)Ω,a(x)∈L∞(Ω)with a(x)>0,φ:=∫Ω1/p(x)(|▽u|p(x)+a(x)|u|p(x)dx,M(t)is a continuous function,(?)u/(?)v is the outer unit normal derivative on (?)Q.b(x),c(x)∈ C(Ω)with b(x),c(x)>0,λ>0 is a real parameter,β(x)∈(0,1)is a continuous function,0<1-β(x)<10 are constants,p ∈ C(Ω)with 10 is a real parameter,c(x),d(x)>0,10 are constants,λ>0 is a real parameter,r(x)∈ C(Ω),1
Keywords/Search Tags:p(x)-Kirchhoff equation, singular nonlinear term, fibering map, mountain pass theorem, Ekeland’s variational principle
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