We study the semiclassical limit of the least energy solutions to the nonlinear Dirac equation in R^3. We prove that the equation has least energy solutions for all small parameters and, in addition, that the solutions converge in a certain sense to the least energy solution of the associated limit problem as the parameter tends to zero.
On semiclassical states of a nonlinear Dirac equation / Y.H. Ding, C. Lee, B. Ruf. - In: PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH. SECTION A. MATHEMATICS. - ISSN 0308-2105. - 143:04(2013), pp. 765-790. [10.1017/S0308210511001752]
On semiclassical states of a nonlinear Dirac equation
B. Ruf
2013
Abstract
We study the semiclassical limit of the least energy solutions to the nonlinear Dirac equation in R^3. We prove that the equation has least energy solutions for all small parameters and, in addition, that the solutions converge in a certain sense to the least energy solution of the associated limit problem as the parameter tends to zero.
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