We prove the existence of a normalized, stationary solution ψ with frequency ω > 0 of a nonlinear Dirac equation. The result covers the case in which the nonlinearity is of Soler type. We find the solution as a critical point of a suitable functional restricted to the unit sphere in L^2 , and ω turns out to be the corresponding Lagrange multiplier.
Normalized solutions for a nonlinear Dirac equation / Coti Zelati, Vittorio; Nolasco, Margherita. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - 414:(2025), pp. 746-772.
Normalized solutions for a nonlinear Dirac equation
Coti Zelati, Vittorio
;Nolasco, Margherita
2025
Abstract
We prove the existence of a normalized, stationary solution ψ with frequency ω > 0 of a nonlinear Dirac equation. The result covers the case in which the nonlinearity is of Soler type. We find the solution as a critical point of a suitable functional restricted to the unit sphere in L^2 , and ω turns out to be the corresponding Lagrange multiplier.File in questo prodotto:
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