Removability of isolated singularities for anisotropic elliptic equations with gradient absorption

We study the well-posedness of the third-order degenerate differential equation (left( {{P_3}} right):alpha {left( {Mu} right)^{prime prime prime }}left( t right) + {left( {Mu} right)^{prime prime }}left( t right) = beta Auleft( t right) + fleft( t right)), (t ∈ [0, 2p]) with periodic boundary conditions (Muleft( 0 right) = Muleft( {2pi } right),;Mu'left( 0 right) = Mu'left( {2pi } right),;Mu''left( 0 right) = Mu''left( {2pi } right)), in periodic Lebesgue–Bochner spaces L^p(T,X), periodic Besov spaces B_p,q^s(T,X) and periodic Triebel–Lizorkin spaces F_p,q^s(T,X), where A, B and M are closed linear operators on a Banach space X satisfying D(A) ( cap )D(B) ? D(M) and α, β, γ ∈ R. Using known operator-valued Fourier multiplier theorems, we completely characterize the well-posedness of (P₃) in the above three function spaces.