Least energy solutions for semilinear Schrdinger equation with electromagnetic fields and critical growth

We study a class of semilinear SchrSdinger equation with electromagnetic fields and the nonlinearity term involving critical growth. We assume that the potential of the equation includes a parameter A and can be negative in some domain. Moreover, the potential behaves like potential well when the parameter A is large. Using variational methods combining Nehari methods, we prove that the equation has a least energy solution which, as the parameter A becomes large, localized near the bottom of the potential well. Our result is an extension of the corresponding result for the SchrSdinger equation which involves critical growth but does not involve electromagnetic fields.

We study a class of semilinear Schrdinger equation with electromagnetic fields and the nonlinearity term involving critical growth.We assume that the potential of the equation includes a parameter λ and can be negative in some domain.Moreover,the potential behaves like potential well when the parameter λ is large.Using variational methods combining Nehari methods,we prove that the equation has a least energy solution which,as the parameter λ becomes large,localized near the bottom of the potential well.Our result is an extension of the corresponding result for the Schrodinger equation which involves critical growth but does not involve electromagnetic fields.