Existence Of Solutions For Two Types Of P-kirchhoff Equations

In this paper,we study the existence of multiple solutions for two types of p-Kirchhoff equations,and at the same time give the energy functional corresponding to the research problem,and further use the variational method to convert the solution of the problem into the energy functional Critical point.The main theoretical basis is the combination of Nehari manifold and Sobolev embedding theorem.The full text mainly includes the following chapters:Chapter 1:A brief introduction to the background of the problem and the current status and development of the research,and gives the theorems and basic knowledge to be used in the article.Chapter 2:The following singular nonlinear p-Kirchhoff equations are discussed:#12 where a is a bounded domain in Rn with smooth boundary ??.1<p<N,?>0 is real parameter.0<?<1,0<?<1,0<?+?<p(m+1)<p*.Chapter 3:The following multiple solution problems of the following singular nonlinear fractional p-Kirchoff equations are discussed:#12The following multiple solution problems of the following singular nonlinear fractional p-Kirchoff equations are discussed:where ? is a bounded domain in RN with smooth boundary ??.N>ps,s ?(0,1),0<?<1,0<?<1,0<?+?<p?<q<p*.?,? are two parameters,a,b,c ? C(?)are non-negative weight functions,M is a continuous function.