Structure of formal solutions of singularly perturbed nth-order differential equations
The authors study the singularly perturbed nth order scalar equation \(\sum^{n}_{i=0}\in^{P_ i}a_ i(t,\epsilon)d^ ix(t,\epsilon)/dt^ i=0,\) under the principal assumptions that \(a_ 0(t,\epsilon)\not\equiv 0\), \(a_ n(t,\epsilon)\not\equiv 0\), \(P_ 0=0\), \(P_ i\geq 0\), \(1\leq i\leq n-1\), and \(P_ n>0\), as \(\epsilon \to 0^+\) by means of Newton diagrams.
singularly perturbed nth order scalar equation
scientific article; zbMATH DE number 3991963