Critcal Exponent for Logarithmic Nonlinearity of Nonlinear Heat Equation

Our aim is to extend the blowup result by Levine-Meier for nonlinear heat equation of Fujita type on conical domains to generalized paraboloidal domains by replacing fractional type nonlinearity to logarithmic one. In this first note we give an abstract result assuring the existence of the critical exponent for such nonlinearity