Search results for "Kirchhoff term"
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Anisotropic Navier Kirchhoff problems with convection and Laplacian dependence
2022
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 respec…
The existence of solutions for the modified (p(x), q(x))-Kirchhoff equation
2022
We consider the Dirichlet problem-Delta(Kp)(p(x))u(x) - Delta(Kq)(q(x))u(x) = f(x, u(x), del u(x)) in Omega, u vertical bar(partial derivative Omega) = 0,driven by the sum of a p(x)-Laplacian operator and of a q(x)-Laplacian operator, both of them weighted by indefinite (sign-changing) Kirchhoff type terms. We establish the existence of weak solution and strong generalized solution, using topological tools (properties of Galerkin basis and of Nemitsky map). In the particular case of a positive Kirchhoff term, we obtain the existence of weak solution (= strong generalized solution), using the properties of pseudomonotone operators.