Morse Index of Solutions of Nonlinear Elliptic Equations (De Gruyter Series in Nonlinear Analysis and Applications; Volume 30) by Lucio Damascelli and Filomena Pacella - 2019

De Gruyter, 2019. Hardbound. New Book. Hardbound. Damascelli (Tor Vergata University of Rome) and Pacella (Sapienza University of Rome) compute the Morse index of radial solutions of classical Lane-Emden problems, show connections between the Morse index of solutions of semilinear elliptic equations and their symmetry properties, and demonstrate symmetry results for solutions of elliptic systems obtained using Morse index bounds. The opening chapters of the graduate text review different forms of weak and strong maximum principles, the classical eigenvalue theory for boundary value problems involving elliptic operators, and basic Morse theory of functions on both finite and infinite dimensional manifolds. (2019 Ringgold, Inc., Portland, OR)