The Existence Of Nontrivial Solutions And Positive Solutions For Generalized Schr(?)dinger Equation With Nonlocal Term

Choquard equation is one of the research objects in the field of nonlinear analysis in recent years,which describing the quantum mechanics of a polaron at rest.In this thesis,we study the existence,of solutions for the generalized quasilinear Schrodinger equations with choquard term and the generalized quasilinear Schrodinger equations with nonlocal term via the variational methods.In chapter 1,we introduce some background,physical sense,notation and mark about our equations.In chapter2,in the case of the pontential function is finitely,by using mountain pass theorem,we prove the existence of the nontrivial solutions for generalized quasilinear Schrodinger equation with choquard term:-div(g2(u)▽u)+g(u)g’(u)|▽u|2+V(x)u=λ[|x|-μ*|u|p]|u|p-2u,x∈RN.In chapter3,in the case of the pontential function is forcing,by implicit functin theorem,we prove the existence of positive solutions for the generalized quasilinear Schrodinger equation with nonlocal term:-div(g2(u)▽u)+g(u)g’(u)|▽u|2+V(x)u=λ[|x|-μ*|u|p-2u,x∈RN.In chapter4,in the case of the pontential function is vanishing at infinity,by using mountain pass theorem,we prove the existence of nontrivial solution for generalized quasilinear Schrodinger equation with choquard term:-div(g2(u)▽u)+g(u)g’(u)|▽u|2+V(x)u=[|x|-μ*(KF(u))]Kf(u),x ∈ R3.