We consider the Navier problem-Delta(2)(k,p)u(x)=f(x,u(x), del u(x), Delta u(x)) in Omega, u vertical bar(partial derivative Omega) =Delta u vertical bar(partial derivative Omega) = 0,driven by the sign-changing (degenerate) Kirchhoff type p(x)-biharmonic operator, and involving a (del u, Delta u)-dependent nonlinearity 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,W-p(x)(Omega)boolean AND W-0(1,p(x))(Omega) leads to the existence result. The case of nondegenerate Kirchhoff type p(x)-biharmonic operator is also considered with respect to the theory of pseudo-monotone operators, and an asymptotic analysis is derived.

Radulescu V.D., Vetro C. (2022). Anisotropic Navier Kirchhoff problems with convection and Laplacian dependence. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 1-18 [10.1002/mma.8521].

Anisotropic Navier Kirchhoff problems with convection and Laplacian dependence

Vetro C.
2022

Abstract

We consider the Navier problem-Delta(2)(k,p)u(x)=f(x,u(x), del u(x), Delta u(x)) in Omega, u vertical bar(partial derivative Omega) =Delta u vertical bar(partial derivative Omega) = 0,driven by the sign-changing (degenerate) Kirchhoff type p(x)-biharmonic operator, and involving a (del u, Delta u)-dependent nonlinearity 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,W-p(x)(Omega)boolean AND W-0(1,p(x))(Omega) leads to the existence result. The case of nondegenerate Kirchhoff type p(x)-biharmonic operator is also considered with respect to the theory of pseudo-monotone operators, and an asymptotic analysis is derived.
Settore MAT/05 - Analisi Matematica
https://onlinelibrary.wiley.com/doi/10.1002/mma.8521
Radulescu V.D., Vetro C. (2022). Anisotropic Navier Kirchhoff problems with convection and Laplacian dependence. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 1-18 [10.1002/mma.8521].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/569007
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