Existence Of Solutions For Kirchhoff-type Elliptic Equations With Critical Exponent And A Class Of Impulsive Equations

As an important part of differential equation theory,the boundary value problem of differential equations has been widely used in physics and biology,and has always been a hot issue in people’s research.By using variational method and critical point theory,this thesis mainly discusses the existence of solutions for Kirchhoff-type boundary value problems under critical conditions and impulsive differential equations.The main research contents of this paper are as follows:Firstly,in Chapter two,we respectively discuss the research status of the two types differential equations,the main work and the corresponding results.Secondly,by using variational method and critical point theory,chapter three studies the existence of solutions for Kirchhoff-type elliptic equations in four-dimensional space under critical conditions.At present,a lot of results on Kirchhoff-type elliptic equations in which the coefficients of the non-linear terms are constants have been obtained.In this chapter,we discuss the equations whose coefficients of non-linear terms are the functions of the independent variable .The results in this chapter compared with previous work are more difficult and complex,which enriched and disseminated relevant research results.Finally,by using variational method and critical point theory,chapter fours studies the existence of solutions for the -Laplacian operator differential equations boundary value problems with impulsive effects.A lot of results on the existence of impulsive differential equation have been obtained by using the method of upper and lower solutions,montone iterative method,fixed point theory,and topological degree theory.However,there are few results on the existence of solutions for impulsive differential equation by using variational method.The results in this chapter compared with previous work are more general,which enriched and extended the relevant results.