ON EXISTENCE OF NODAL SOLUTION TO ELLIPTIC EQUATIONS WITH CONVEX-CONCAVE NONLINEARITIES

In a bounded connected domain Omega subset of R-N, N >= 1 , with a smooth boundary, we consider the Dirichlet boundary value problem for elliptic equation with a convex -concave nonlinearity {-Delta u = lambda vertical bar u vertical bar(q-2)u + vertical bar u vertical bar(gamma-2)u, x is an element of Omega u vertical bar(delta Omega) = 0, where 1 < q < 2 < gamma < 2*. As a main result, we prove the existence of a nodal solution to this equation on the nonlocal interval lambda is an element of (-infinity, lambda(*)(0)), where lambda(*)(0) is determined by the variational principle of nonlinear spectral analysis via fibering method.