Homogeneous multidimensional differential systems for mathematical models

Strictly Cooperative Systems with a First Integral

“…On the other side, many authors (e.g. [5], [6], [7], [9], [10]) considered cooperative (or related) systems on the nonnegative orthant g having Yi xi as a first integral. For such systems it was proved that every solution converges to an equilibrium.…”

Existence and Stability of Almost Periodic Solutions in Almost Periodic Systems

“…Now we shall prove the uniqueness of (f>j. Suppose (f>i=/=(f>j for _y'^>2 hand, (3)(4)(5)(6)(7)(8)(9)(10)(11)(12) shows that fl = *SiU*5 2 , which contradicts the connectedness of J2. Thus the uniqueness of an almost periodic solution is proved, and moreover, as is seen from [7], this uniqueness guarantees the module containment of the almost periodic solution.…”

“…Especially, in the case where <2y(£) in system (1-1) are constants, the system governs one of mathematical models of gas dynamics (cf. [2, p. 104] ) and has been studied by Jenks [4] . One of Jenks' results is a special case of Theorem 2.…”

Dynamical Systems Under Constant Organization II: Homogeneous Growth Functions of Degree $p = 2$

“…We have to thank the referee for pointing out that the restriction of (1.2) on S, coincides there with a type of equation studied by Jenks in [8]- [10]. Indeed, using xi 1, we may write (1.2) in the form…”