Existence Of Solutions For Two Classes Of Schrodinger Equations In R~N With Magnetic Field

We considered the following Schrodinger equations(?)where N?3,K:RN?R is a nonnegative function,f:R?R has subcritical growth,the potential V:IRN?R is nonnegative.We established a result on existence of solutions for two classes of Schrodinger equations in RN with magnetic field.We studied the problem with vanishing potential,namely(?)where K?1,and lim|x|??,V=0.The variational method combined with penalization technique of Del Pino and Moser iteration is used to deal with the problem with magnetic field and vanishing potential.Assume that V (?) 0.We investigated the following Schrodinger equations(?)where f is a continuous function verifying condition f'(0)=0,which is known as zero mass.We discussed the equations with K asymptotically periodic and K ?Lr.The techniques used here are variational methods and some technical lemmas based on Lions' lemma.