Bifurcation of nonlinear elliptic system from the first eigenvalue, Electron
We study the following bifurcation problem in a bounded domain in IR N : 8 : pu = juj jvj v + f(x; u; v; ) in qv = juj jvj u + g(x; u; v; ) in (u; v) 2 W 1;p 0 () W 1;q 0 () : We prove that the principal eigenvalue 1 of the following eigen- value problem 8
It is shown that a finite-amplitude ion-acoustic wave in a uniform magneto- plasma can enhance two-dimensional plasma vortices. The latter results from a modulational instability. The growth rates are obtained analytically.