Integral stability criteria of nonlinear differential systems

The notions of equi-integral and ϕ0ϕ0-stability for systems of ordinary differential equations (ODEs) were introduced and extended. The notions of equi-integral stability are extended to the so-called equi-integral ϕ0ϕ0-stability of perturbed system of (ODEs). Our technique depends on cone-valued Liapunov function method.