Article - postprint
Sign-changing solutions to semilinear elliptic problems in connection with their Morse indices. To this end, we first establish a priori bounds for one-sign solutions. Secondly, using abstract saddle point principles we find large augmented Morse index solutions. In this part, extensive use is made of critical groups, Morse index arguments, Lyapunov-Schmidt reduction, and Leray-Schauder degree. Finally, we provide conditions under which these solutions necessarily change sign and we comment about further qualitative properties.
© 2013 American Institute of Mathematical Sciences
Castro, Alfonso, Jorge Cossio and Carlos Velez. "Existence and Qualitative Properties of Solutions for Nonlinear Dirichlet Problems", to appear in Continuous and Discrete Dynamical Systems, Series A.