Anisotropic Navier Kirchhoff problems with convection and Laplacian dependence

Autor:	Vicenţiu D. Rădulescu, Calogero Vetro
Přispěvatelé:	Radulescu V.D., Vetro C.
Rok vydání:	2022
Předmět:	Galerkin approximation method pseudomonotone operator Settore MAT/05 - Analisi Matematica General Mathematics General Engineering Kirchhoff term p(x)-biharmonic operator Brouwer fixed point theorem Nemitsky map
Zdroj:	Mathematical Methods in the Applied Sciences. 46:461-478
ISSN:	1099-1476 0170-4214
DOI:	10.1002/mma.8521
Popis:	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.
Databáze:	OpenAIRE
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