\((h_0,h,M_0)\)-uniform stability properties for nonlinear differential systems (Q1862679)

Lakshmikantham and Liu introduced a very general type of stability, called (\(h_0,h\))-stability, by combining the concepts of \(M_0\)-stability and (\(h_0,h,M_0\))-stability and presented a comparison result cocerning (\(h_0,h,M_0\))-uniform asymptotic stability. However, very little is known about (\(h_0,h,M_0\))-uniform stability properties when the comparison principle fails. This paper is devoted to the development of a basic theory of Lyapunov in terms of (\(h_0,h\))-uniform asymptotic stability employing Lyapunov's direct method.