The paper studies the special classes of the stationary and nonstationary solutions of VM system and their connection with the systems of nonlocal semilinear elliptic equations with boundary conditions. Using the proposed lower-upper solution method, we proved an existence theorem for a semilinear nonlocal elliptic boundary value problem under corresponding restrictions over the distribution function (ansatz RSS 52, 53).

Key words: Vlasov-Maxwell system, boundary value problem, upper-lower solution.

El artículo estudia clases especiales de soluciones estacionarias y no estacionarias de sistemas VM y su conexión con los sistemas semilineales elípticos no locales con condiciones de frontera. Usando el método de bajo-alto demostramos un teorema de existencia para un problema elíptico semilineal no local con valor de frontera bajo las restricciones correspondientes sobre la función de distribución (ver ansatz RSS 52, 53)

Palabras clave: Sistema Vlasov-Maxwell, problema del valor límite, solución superior-inferior.

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