Oscillation and nonoscillation criteria for differential equations of second order
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We give necessary and sufficient conditions such that the homogeneous differential equations of the type: (r(t)x'(t))' + q(t)x'(t) + p(t)x(t) = 0are nonoscillatory where r(t) >0 for t ∈ I = [α, ∞), α > 0. Under the suitable conditions we show that the above equation is nonoscillatory if and only if for γ > 0, (r(t)x'(t))' + q(t)x'(t) + p(t)x(t - γ) = 0 is nonoscillatory. We obtain several comparison theorems.
Abstract
We give necessary and sufficient conditions such that the homogeneous differential equations of the type: (r(t)x'(t))' + q(t)x'(t) + p(t)x(t) = 0are nonoscillatory where r(t) >0 for t ∈ I = [α, ∞), α > 0. Under the suitable conditions we show that the above equation is nonoscillatory if and only if for γ > 0, (r(t)x'(t))' + q(t)x'(t) + p(t)x(t - γ) = 0 is nonoscillatory. We obtain several comparison theorems.
참고문헌 (12)
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