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math.AP2025
Electron beams: partially flat solutions of a nonlinear elliptic equation with a singular absorption term
Jesús Ildefonso Díaz
In the so-called Child-Langmuir law, established since 1911, an electron beam is formed linking two electrodes, which are assumed to be two parallel plates of area , separated t…
math.AP2025
On the compactness of the support of solitary waves of the complex saturated nonlinear Schr{ö}dinger equation and related problems
Pascal Bégout, Jesús Ildefonso Díaz
We study the vectorial stationary Schr{ö}dinger equation -u + a U + b u = F, with a saturated nonlinearity U = u/|u| and with some complex coefficients (a, b) C 2 . Beside…