Existence And Concentration Of Ground State Solutions For A Schr(?)dinger Logarithmic Equation

In this dissertation,we study the following logarithmic Schr(?)dinger equation with disturbance term-?u+?V(x)u=u logu2+f(u),x?RN,where ?>0,N>1,V:RN?R is a potential,nonlinear term f satisfy some conditions.Due to the existence of the logarithmic term u log u2,the functional corresponding to the equation is lost C1 Smoothnesson H1(RN)so we use the variational method developed by Szulkin for functionals,which are the sum of a C1 functional with a convex lower semicontinuous functional.When the positive parameter ? is sufficiently large,we get the existence of a ground state solution for the equation using the Mountain Pass theorem without(PS)condition.Then,when the nonlinear term f still satisfies the monotonicity condition,We prove the concentration of the ground state solution for the above equation using Nehari set,i.e.as ?n?+?,the ground state solution u??u? in H1(RN),where u??0,a.e.in RN\?,?:=intV-1(0),and u? is a nontrivial solution of the limit problem(?) This result generalizes the existence and the concentration of ground state solutions for the Schr(?)dinger equation about Alves et al[Math.Methods Appl.Sci.,2019],Yin and Wu[Comput.Math.Appl.,2019].