A critical behavior for some semilinear parabolic equations involving sign changing solutions (Q1612615)

The paper deals with sign changing solutions to the Cauchy problem \[ \begin{cases} \Delta u+|u|^p-u_t=0, & \text{ in } {\mathbb R}^n\times(0,\infty),\cr u(x,0)=u_0(x), & \text{ in } {\mathbb R}^n.\end{cases} \] The author provides a condition under which the problem possesses global or blowing up solutions.