BIHARMONIC-KIRCHHOFF TYPE EQUATION INVOLVING CRITICAL SOBOLEV EXPONENT WITH SINGULAR TERM
Commun. Korean Math. Soc.
Published online January 21, 2021
Kamel Tahri and Fares Yazid
Abou Bekr Belkaid Univ, Tlemcen, Amar Teledji University, Laghouat
Abstract : Using variational methods, we show the existence of a unique weak solution of the following singular biharmonic problems of Kirchhoff type involving critical Sobolev exponent:

(P_{λ}){<K1.1/>┊

<K1.1 ilk="MATRIX" >
Δ²u-(a∫_{Ω}|∇u|²dx+b)Δu+cu=f(x)|u|^{-γ}-λ|u|^{p-2}u in Ω,
Δu=u=0 on ∂Ω.
</K1.1>
where Ω is a smooth bounded domain of ℝⁿ (n≥5), Δ² is the biharmonic operator, and ∇u denotes the spatial gradient of u and 0<γ<1, λ>0, 0<p≤2^{♯} and a,b,c are three positive constants with a+b>0 and f belongs to a given Lebesgue space.
Keywords : Variational methods, critical Sobolev exponent, biharmonic operator, Kirchhoff equations.
MSC numbers : 35A15
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