On a general class of p(x)-Kirchhoff equations with nonstandard growth conditions

This paper deals with a general class of p ( x ) -Kirchhoff equations with nonstandard growth conditions, where the general Kirchhoff function encompasses both non-degenerate and degenerate cases. We establish some results concerning the energy decay and finite time blow-up of weak solutions in the case of low initial energy. We also provide a sufficient condition that leads to the blow-up phenomenon with arbitrary initial energy. Our results substantially improve and generalize recent work by Chuong et al. [8] , and they also resolve the open problem raised in [1] .