Evolution inclusions governed by the difference of two subdifferentials in reflexive Banach spaces

The applicability of our abstract framework will be exemplified in discussing the existence of solutions for the nonlinear heat equation: ut(x,t)-Δpu(x,t)-|u|q-2u(x,t)=f(x,t),x∈Ω,t>0,u|∂Ω=0, where Ω is a bounded domain in RN. In particular, the existence of local (in time) weak solution is shown under the subcritical growth condition q