Generalized Budan-Fourier theorem and virtual roots
In this Note we give a proof of a generalized version of the classical Budan-Fourier theorem, interpreting sign variations in the derivatives in terms of virtual roots.
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