Solutions of asymptotically linear operator equations via morse theory

1981/09/01 by Kung Ching Chang · 197 citations
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Calculus (dental) #Citation #Computer science #Library science #Mathematics #Morse code #Operator (biology) #Spectral Theory in Mathematical Physics #Telecommunications #advanced mathematical theories

paper · doi:10.1002/cpa.3160340503

published in Communications on Pure and Applied Mathematics 34(5), 693-712 (Wiley)

openalex publication_date 1981/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/25

Abstract

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)

Cited by

• Morse‐type index theory for flows and periodic solutions for Hamiltonian Equations
• Some critical point theorems and applications
• Periodic solutions to Klein-Gordon systems with linear couplings
• Infinitely many periodic solutions for a semilinear wave equation with x-dependent coefficients
• Index theory for linear self-adjoint operator equations and nontrivial solutions for asymptotically linear operator equations

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• Index theory for linear self-adjoint operator equations and nontrivial solutions for asymptotically linear operator equations(II)
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• Multiplicity results and qualitative properties for semilinear elliptic problems with Neumann boundary conditions
• Existence and Multiplicity of Solutions for a Cooperative Elliptic System Using Morse Theory