Existence And Concentration Of Semiclassical States For Kirchhoff-Poisson Equations

We study the following two kinds of semi-classical Kirchhoff-Poisson equations:(?),where ε>0 is a parameter,a,b>0 are constants,4<p<6,and the potentials K∈C((?)~3,(?)),V∈C((?)~3,(?)),V≥0.and (?),where ε>0 is a parameter,a,b>0 are constants,2<p<3,and the potentials K∈C((?)~3,(?)),V∈C((?)~3,(?)),V≥0.In the second chapter,it proved the functional of equation(P)satisfies(PS)_C condition whenV,K satisfy certain conditions and parameter ε>0 is small,which proves that equation()has a positive groundstate solution.In the third chapter,it proved the equation(C_ε) has a positive groundstate solution by proving the convergence of the minimized sequence.Meanwhile,it exhibited the concentration behavior of the solution of equation (C_ε) as ε→0 by describing the limiting function and the concentrated function.