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Principal solutions and minimal sets of quasilinear differential equations. (English) Zbl 1123.34026
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.

MSC:
34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
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