
Summary: We present sufficient conditions for property (B) and the oscillation of the third-order nonlinear functional differential equation with mixed arguments \[ [a(t)[x'(t)]^\gamma]'' = q(t)f(x[\tau(t)]) + p(t)h(x[\sigma(t)]), \] where \(\int^\infty a^{-1/\gamma}(s)\,\text{d}s = \infty\). We deduce properties of the studied equations by establishing new comparison theorems so that property (B) and the oscillation are resulting from the oscillation of suitable first-order equations.
Oscillation, Asymptotic theory of functional-differential equations, nonoscillation, Third-order functional differential equations, Oscillation theory of functional-differential equations, Comparison theorem, comparison theorem, oscillation, third-order functional differential equations
Oscillation, Asymptotic theory of functional-differential equations, nonoscillation, Third-order functional differential equations, Oscillation theory of functional-differential equations, Comparison theorem, comparison theorem, oscillation, third-order functional differential equations
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