Solutions of asymptotically linear operator equations via morse theory
Kung-Ching Chang · Communications on Pure and Applied Mathematics · 1981
In this paper, we use the classical Morse theory of critical points to study the existence and multiplicity of solutions of a class of asymptotically linear operator equations. As special cases, we include multiplicity results for semilinear elliptic BVP's, as well as existence and multiplicity of periodic solutions of semilinear wave equation and of Hamiltonian systems. These results simplify and complement recent work of Amann Zehnder and Castro Lazer. (Author)