A note on the monotonicity of the Maslov-type index of linear Hamiltonian systems with applications
Chungen Lıu · Proceedings of the Royal Society of Edinburgh Section A Mathematics · 2005
In this note, we first consider the monotonicity of the Maslov-type index theory. More precisely, for any two 1-periodic symmetric continuous matrix functions B0(t) and B1(t) with B0(t) < B1(t), we consider the relations between the Maslov-type indices (i(B0), ν (B0)) and (i(B1), ν (B1)). We then apply this theory to study the existence and multiplicity of some kinds of asymptotically linear Hamiltonian systems