Qualitative properties of nodal solutions of semilinear elliptic equations in radially symmetric domains. C. R. Math. Acad. Sci. Paris

Abstract We study the qualitative properties of sign changing solutions of the Dirichlet problem u+f(u) = 0 in , u = 0 on @ , where is a ball or an annulus and f is a C1 function with f(0) 0. We prove that any radial sign changing solution has a Morse index bigger or equal to N + 1 and give sufficient conditions for the nodal surface of a solution to intersect the boundary. In particular, we prove that any least energy nodal solution is non radial and its nodal surface touches the boundary