Generic properties of the Fucik spectrum of elliptic operators

Given a bounded smooth domain Omega subset of R-n, n greater than or equal to 2, and a second-order elliptic self-adjoint operator A on Omega, the set of points (alpha, beta) is an element of R-2 for which the problem Au = al pha u(+) - beta u(-) in Omega, u = 0 on partial derivative Omega (where u(/-) = max{+/-u, 0}), has a non-trivial solution is called the Fucik spectru m of A. In this note we extend some recent results of Pistoia on the struct ure of this set for generic operators A (the genericity is with respect to the domain Omega or the coefficients of A).