170 research outputs found
On nodal radial solutions of an elliptic problem involving critical Sobolev exponent
summary:In this paper we construct radial solutions of equation (1) (and (13)) having prescribed number of nodes
Existence results for quasilinear Dirichlet problem
This paper deals with the Dirichlet problem (1) -Σ D(a(x, u) D1u) + c(x)u = b(x, u, Du) in Q. (2) n(x)=ф(x) on ∂Q. in a bounded domain Q⊂R,n with the boundary ∂Q of class C2 and a function ф which, in general, ..
Magnetic Monopoles, Electric Neutrality and the Static Maxwell-Dirac Equations
We study the full Maxwell-Dirac equations: Dirac field with minimally coupled
electromagnetic field and Maxwell field with Dirac current as source. Our
particular interest is the static case in which the Dirac current is purely
time-like -- the "electron" is at rest in some Lorentz frame. In this case we
prove two theorems under rather general assumptions. Firstly, that if the
system is also stationary (time independent in some gauge) then the system as a
whole must have vanishing total charge, i.e. it must be electrically neutral.
In fact, the theorem only requires that the system be {\em asymptotically}
stationary and static. Secondly, we show, in the axially symmetric case, that
if there are external Coulomb fields then these must necessarily be
magnetically charged -- all Coulomb external sources are electrically charged
magnetic monopoles
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