Research On The Existence And Multiplicity Of Solutions For A Class Of Elliptic Equation With Neumann Boundary Value Problems

In this paper,the existence and multiplicity of solutions for a class of elliptic equation with Neumann boundary value problems are studied by variational methods,truncation techniques,Nehari’s methods,etc.Firstly,we consider the existence of solutions for the following type of Kirchhoff-type equations on with Neumann boundary value problems (?) where Ω(?)RN is a bounded domain with smooth boundary(N≥1),v is the external normal unit vector,a＞ 0,b≥0,λ＞ 0,1 ＜q＜2 are real parameters.The existence and multiplicity of solutions to the equation(0.4)are obtained by variational methods and truncation techniques.Secondly,we generalize the equation(0.4)to the following Neumann problem(?)where c(x)is a sign-changing potential,a,b≥0 and a+b＞ 0,1＜q＜2.The existence and multiplicity of solutions to equation(0.5)are also obtained through vari-ational methods and truncation techniques.Finally,we study the following Neumann boundary value problems with singular terms and critical growth(?)where Ω(?)RN is a bounded smooth domain(N≥3),0<γ<1,λ>0 are parameter,0<a(x)∈ L∞((?)Ω)is a non-negative function,and v is the external normal unit vector.The existence of two positive solutions to the equation(0.6)is obtained by variational methods and Nehari’s methods.