Cecchi, Mariella; Dǒslá, Zuzana; Marini, Mauro Principal solutions and minimal sets of quasilinear differential equations. (English) Zbl 1123.34026 Dyn. Syst. Appl. 13, No. 2, 221-232 (2004). The authors consider the quasilinear differential equation \[ (a(t)\Phi_p(x'))'=b(t)\Phi_n(x),\qquad t\geq 0,\tag{1} \]where \(a\), \(b\) are positive continuous functions, \(p\), \(n>1\) are real numbers, and \(\Phi_p(u)=| u| ^{p-2}u\). The equivalence of the limit, Riccati, and integral characterizations of principal solutions to \((1)\) is proved in the case \(p=n\). The notion of principal solution is extended to a class of quasilinear differential equations. Reviewer: Aleksandr Lomtatidze (Brno) Cited in 3 Documents MSC: 34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations Keywords:Half-linear differential equation; quasilinear differential equation; principal solution; limit behaviour PDFBibTeX XMLCite \textit{M. Cecchi} et al., Dyn. Syst. Appl. 13, No. 2, 221--232 (2004; Zbl 1123.34026)