On the weak solution for the nonlocal parabolic problem with p-Kirchhoff term via topological degree

In this work, we study the existence of weak solution for the following nonlinear parabolic initial boundary value problem associated to the p -Kirchhoff -type equation, (partial derivative u)/(partial derivative t) - M(integral(Omega)( A(x,t del mu)+(1)/(p)|mu|(p))dx)div(a(M A(x, t, del u) - |del u| (p-2) |u|p del u) = f in Q. = ohm x(0, T) where ohm subset of R-n (N >= 2) is a bounded domain with Lipschitz boundar partial derivative ohm, M : R+ -> R+ is the p -Kirchhoff -type function and a : Q x R-N -> R-N is a Carathe<acute accent>odory function. Under some appropriate assumptions, we obtain the existence of a weak solution for the problem above by using Berkovits and Mustonen topological degree theory, in the space L-p(0, T, W-1,W-p (0 )(ohm)).