Existence Of Solutions To Two Kinds Of Critical Growth Equations

In this dissertation,we study the existence of ground state solutions for the following two classes of critical growth equations.In the first,we study the following Schr(?)dinger-Poisson system:(?)where 4<p<5 and V(x),k(x)is a smooth function.By employing constraint variational method and a variant of the classical deformation lemma,we show the existence of one ground state sign-changing solution with precisely two nodal domains.Then we concern with the following Kirchhoff-Schr(?)dinger-Poisson systems with critical growth:(?)where V(x)is a smooth function and a>0,b>0,p ∈[4,6)and λ>0 is a parameter.By employing nodal Nehari manifold technique,for each b>0,we obtain a least energy nodal solution ub and a ground-state solution vb to this problem when k(?)1.Moreover,we also study the asymptotic give behavior of ub as the parameter b→0.