Normalized Solutions To Two Kinds Of Equations

In the first chapter,we briefly introduce the research background and the main results.In the second chapter,we study the following nonlinear mass supercritical Kirchhoff equation(?)(P1)satisfying the normalized constrain ∫RN|u|2dx=m in the case 1≤N≤ 3 and a,b,m>0 prescribed.The nonlinearity f is more general.Under some mild assumptions,we establish the existence of ground state when 1≤N≤3 and obtain infinitely many radial solutions when 2≤N≤3 by constructing a particular bounded Palais-Smale sequence.In the third chapter,we consider the following nonlinear mass supercritical Schr(?)dingerPoisson-Slater equation-Δu+μu-γ(|x|-1*|u|2)u-af(u)=0 x∈R3(P2)satisfying the normalized constrain ∫R3|u|2dx=m,and m>0 prescribed.The nonlinearity f is super-critical.Under some mild assumptions,we establish the existence of ground state and infinitely many radial solutions by constructing a particular bounded Palais-Smale sequence when γ<0,a>0.Meanwhile,we obtain the non-existence result in the caseγ<0,a<0 and the existence result when γ>0,a<0 via variational methods.