On the T-nature of differential inequalities (Q1177737)

The paper deals with the properties of \(n\)-dimensional subspaces of \(C[a,b]\) spanned by the \(T_{n-1}\)-system of functions \(\{\varphi_ i(t)\}^{n-1}_{i=0}\) (a system of functions \(\{\varphi_ i(t)\}^{n- 1}_{i=0}\) is said to be a \(T_{n-1}\)-system if every linear combination of \(\varphi_ 0,\dots,\varphi_{n-1}\) has at most \(n-1\) different zeros on \([a,b]\)). It is shown that functions from such subspaces behave like solutions of \(n\)-th order disconjugate differential equations. The results presented in the paper complete and generalize some results given in the second author's paper [Math. Notes 43, No. 5, 355-359 (1988); translation from Mat. Zametki 43, No. 5, 615-623 (1988; Zbl 0708.41007)].