Disconjugacy and nonoscillation domains for nonlinear singular interface problems on semi-infinite time scales (Q410605)

Summary: We define and discuss the disconjugacy \((\mathcal D)\) and nonoscillation \((\mathcal N)\) domains for a pair of dynamic equations along with matching interface conditions on the semi-infinite time scale \([0, c]_{\mathbb T} \cup [\sigma (c), \infty]_{\mathbb T}\). We show that these domains are closed and convex subsets of the parameter space \(\mathbb R^{n+m}\). The theory developed is used to discuss the oscillatory behavior of initial and boundary value problems associated with interface problems in the fields of applied elasticity, acoustic wave guides in ocean, and transverse vibrations in strings.