The Maximum Principle and Sign-Changing Solutions of the Klein-Gordon Equation with the Higgs Potential in the de Sitter Spacetime

摘要

In this chapter, we discuss the maximum principle for the linear equation and the sign-changing solutions of the semilinear equation with the Higgs potential. Numerical simulations indicate that the bubbles for the semilinear Klein-Gordon equation in the de Sitter spacetime are created and apparently exist for all times.