A Multiplicity result for a class of strongly indefinite asymptotically linear second order systems

TL;DR

This paper establishes multiple solutions for a class of strongly indefinite, asymptotically linear second order systems using a novel combination of the shooting method and Maslov index techniques.

Contribution

It introduces a new approach by integrating the shooting method with Maslov index theory to prove multiplicity results for nonlinear systems.

Findings

Proved existence of multiple solutions for the class of systems studied.

Developed a novel proof technique combining classical shooting and Maslov index.

Extended the understanding of asymptotically linear systems with indefinite characteristics.

Abstract

We prove a multiplicity result for a class of strongly indefinite nonlinear second order asymptotically linear systems with Dirichlet boundary conditions. The key idea for the proof is to bring together the classical shooting method and the Maslov index of the linear Hamiltonian systems associated to the asymptotic limits of the given nonlinearity.