Meleshko, "Linearization of second-order ordinary differential equations by generalized sundman transformations," Symmetry, Integrability
and Geometry: Methods and Applications (SIGMA), vol.
In Section 3, Theorems 12 and 13 show the local higher integrability
of commutators of Calderoon-Zygmund singular integral operators on differential forms.
Valls, "On the local analytic integrability
at the singular point of a class of Lionard analytic differential systems," Proceedings of the American Mathematical Society, vol.
Since the ultimate goal is to study nonlinear systems, and not the globally linearized equations, the conditions similar to linear theory are accompanied with certain integrability
To continue, we recall that the integrability
of J is equivalent to the following equality
Differential-geometric approach to the integrability
of hydrodynamic chains: the Haantjes tensor.
Burton  discussed the stability, boundedness, convergence of bounded solutions and square integrability
of solutions of equation (1.2) by defining a Lyapunov functional.
In soliton theory, the study of integrability
to nonlinear evolution is always a hot topic of interest, which can be regarded as a key step of their exact solvability.
The role of these first integrals is often crucial in the study of solutions and properties of differential equations, including questions related to stability [9,10] or integrability
The aim of this paper is to generalize AKNS spectral problem (4) and its evolution equation (5) for testing the integrability
of the following new and more general non-isospectral integrodifferential system:
Now we give a related result, replacing the boundedness condition of f by certain integrability
conditions of f and of (EQ.).
The topics include approaching monotone inclusion problems via second order dynamical systems with linear and anisotropic damping, differentiability and integrability
properties for solutions to non-local equations, sliding modes for a phase-field system, equilibrium in an individual-societal susceptible-infected-recovered vaccination model in the presence of discounting and finite vaccination capacity, and singularly perturbed problems for abstract differential equations of second-order in Hilbert spaces.