Non–limit‐circle and limit‐point criteria for symplectic and linear Hamiltonian systems

Abstract

AbstractSeveral necessary and/or sufficient conditions for the existence of a non–square‐integrable solution of symplectic dynamic systems with general linear dependence on the spectral parameter on time scales are established and a sufficient condition for the limit‐point case is derived. Almost all presented results are new even in the continuous and discrete cases, that is, for the linear Hamiltonian differential systems and for the discrete symplectic systems, respectively.