This paper studies nonexistence of nontrivial nonnegative weak solutions for an inhomogeneous nonlocal weighted parabolic differential inequality in the whole space, involving p-Laplacian type quasilinear operator and the weight functions may be singular or degenerate at the origin. In the framework of test functions theory, modifying the nonlinear capacity method to derive precise a priori estimates and establish a new Fujita-type nonexistence theorem.

This paper investigates a semilinear damped σ-evolution differential inequality with space-time varying coefficients in the whole space. Based on the appropriate selection of test functions, we establish new a prior estimates and obtain the nonexistence of the global weak solutions and the upper bound of lifespan estimates of the local weak solutions.