Nonlinear Perron-Frobenius problem. An extension of Morishima's theorem (Q799850)

Homogeneous systems of differential equations \(du_ j/dt=A_ j(u_ 1,...,u_ n)-\mu u^ 2_ j\), \(j=1,...,n\), where \(A_ j(u)\) is a quadratic form, are studied. The author introduces the notion of non- sectionality which is wider than that of indecomposability defined by economists. Using this concept, the eigenvalue problem of the form \(H(u)=\lambda u (H_ j(u)=A_ j(u)^{1/2}\), \(\lambda =\mu^{1/2})\) is investigated.