Solutions of Asymptotically Linear Operator Equations via Morse Theory.
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WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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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 BVPs, 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
- Theoretical Mathematics