We study the stationary Dirac equation with a matrix potential describing the external field, and a asymptotically quadratic nonlinearity modelling various types of interaction without any periodicity assumption. Our discussion includes the Coulomb potential as a special case, and for the semiclassical situation we handle the scalar fields. We obtain existence and multiplicity results of stationary solutions via critical point theory.
Solutions of a nonlinear Dirac equation with external fields / Yanheng Ding, B. Ruf. - In: ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS. - ISSN 0003-9527. - 190:1(2008), pp. 57-82. [10.1007/s00205-008-0163-z]
Solutions of a nonlinear Dirac equation with external fields
B. RufUltimo
2008
Abstract
We study the stationary Dirac equation with a matrix potential describing the external field, and a asymptotically quadratic nonlinearity modelling various types of interaction without any periodicity assumption. Our discussion includes the Coulomb potential as a special case, and for the semiclassical situation we handle the scalar fields. We obtain existence and multiplicity results of stationary solutions via critical point theory.
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