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- W4285012605 abstract "We consider the Navier problem − Δ k , p 2 u ( x ) = f ( x , u ( x ) , ∇ u ( x ) , Δ u ( x ) ) in Ω , u ∂ Ω = Δ u ∂ Ω = 0 , $$ -{Delta}_{k,p}^2u(x)=fleft(x,u(x),nabla u(x),Delta u(x)right)kern0.30em mathrm{in}kern0.5em Omega, kern0.30em u{left|{}_{mathrm{partial Omega }}=Delta uright|}_{mathrm{partial Omega }}=0, $$ driven by the sign-changing (degenerate) Kirchhoff type p ( x ) $$ p(x) $$ -biharmonic operator, and involving a ( ∇ u , Δ u ) $$ left(nabla u,Delta uright) $$ -dependent nonlinearity f $$ f $$ . We prove the existence of solutions, in weak sense, defining an appropriate Nemitsky map for the nonlinearity. Then, the Brouwer fixed point theorem assessed for a Galerkin basis of the Banach space W 2 , p ( x ) ( Ω ) ∩ W 0 1 , p ( x ) ( Ω ) $$ {W}^{2,p(x)}left(Omega right)cap {W}_0^{1,p(x)}left(Omega right) $$ leads to the existence result. The case of nondegenerate Kirchhoff type p ( x ) $$ p(x) $$ -biharmonic operator is also considered with respect to the theory of pseudo-monotone operators, and an asymptotic analysis is derived." @default.
- W4285012605 created "2022-07-12" @default.
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- W4285012605 date "2022-07-10" @default.
- W4285012605 modified "2023-10-05" @default.
- W4285012605 title "Anisotropic Navier Kirchhoff problems with convection and Laplacian dependence" @default.
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- W4285012605 doi "https://doi.org/10.1002/mma.8521" @default.
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