Existence Of Solutions To The Neumann Boundary Value Problem For A Class Of Elliptic Equations

In this thesis,we are concerned with the following Neumann boundary problem where ?(?)RN is a bounded domain with smooth boundary and n denotes the outward normal vector on(?)? and ? are positive constants and ?? R\{0},and K(x)is a positive function in C2(?)? C1(?).Without loss of generality,we set c=1.Then we will prove the following two conclusions.When ?<0 and N? 1,the system has a unique solution.Particularly,the solution is a constant if and only if K(x)is a constant.When ?>0 and N=2,there is a mountain-pass solution if ? is sufficient small,and there are either boundary(or interior)peak solutions as??0.