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Existence of eventually positive solutions of fourth order quasilinear differential equations. (English) Zbl 1244.34054
Continuing his earlier investigations the author establishes some necessary and sufficient conditions for the existence of eventually positive solutions of the equation \[ (p(t)|u''|^{\alpha -1} u'')''+q(t) |u|^{\beta -1} u = 0 . \] Here \(p(t)\), \(q(t)\) are positive continuous functions defined on \([a,\infty )\), \(a>0\), \(\alpha \), \(\beta \) are positive constants.

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