Second-order half-linear delay differential equations: Oscillation tests
Keywords:
Oscillation, nonoscillation, delay, half-linear, Lebesgue's dominated convergence theoremAbstract
In this work, we obtain necessary and sufficient conditions for the oscillation of all solutions of second-order half-linear delay differential equation of the form ( r ( y ′ ) γ ) ′ ( t ) + q ( t ) y α ( τ ( t ) ) = 0 . We study this equation under the assumption ∫ ∞ ( r ( η ) ) − 1 / γ d η = ∞ and consider two cases when γ > α and γ < α . We provide examples, illustrating the results and state an open problem.
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