The paper is devoted to the study of singularly perturbed fractional Schrödinger equations involving critical frequency and critical growth in the presence of a magnetic field. By using variational methods, we obtain the existence of mountain pass solutions uε which tend to the trivial solution as ε → 0. Moreover, we get infinitely many solutions and sign-changing solutions for the problem in absence of magnetic effects under some extra assumptions
Binlin, Z., Squassina, M., Xia, Z., Fractional NLS equations with magnetic field, critical frequency and critical growth, <<MANUSCRIPTA MATHEMATICA>>, 2017; (155): 115-140. [doi:10.1007/s00229-017-0937-4] [http://hdl.handle.net/10807/116456]
Fractional NLS equations with magnetic field, critical frequency and critical growth
Squassina, Marco
Penultimo
;
2017
Abstract
The paper is devoted to the study of singularly perturbed fractional Schrödinger equations involving critical frequency and critical growth in the presence of a magnetic field. By using variational methods, we obtain the existence of mountain pass solutions uε which tend to the trivial solution as ε → 0. Moreover, we get infinitely many solutions and sign-changing solutions for the problem in absence of magnetic effects under some extra assumptions
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