The Multiplicity Of Solutions To K-Hessian Equations

The k-Hessian equation is a type of fully nonlinear partial differential equation.Its own research results play a key role in the development of differential geometry and applied science.It is also very important to explore the multiple solutions of the k-Hessian equations.Firstly,we introduce the research background and the research status of the multiplicity of solutions to k-Hessian equations.Secondly,we introduce the basic concepts and lemmas involved in the research process.Finally,we prove the existence and multiplicity for k-admissible solutions of the k-Hessian equations and the multiplicity for radial solutions of superlinear equations with critical terms.