Research On The Normalized Solutions For A Nonlocal Problem

In this thesis,we study the non-existence,existence and multiplicity of solution-s,including positive solutions and sign-changing solutions,to the following Kirch-hoff type equation by analysis method (?) where N?N+ denotes the space dimension,a,b,c are fixed positive constants,??R is a parameter and p ?(0,2*-2),(?)if N? 3 and 2*?+? if N?1,2.What's more,we also give the characterization of the solutions if it exists.Our results can be seen as a complement to that shown by[1-3].