Klein-Gordon Equation with Critical Initial Energy and Nonlinearities with Variable Coefficients
摘要
In this paper, we focus on the global behavior of the weak solutions to the Cauchy problem for Klein-Gordon equation with critical initial energy. We consider the polynomial-type nonlinearities with coefficients, depending on the space variables. All coefficients have a constant sign, except one of them, which may change its sign. By means of the sign-preserving properties of the Nehari functional and the concavity method, we prove nonexistence of global solutions or non-blowing up of the weak solutions.