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AbstractWe examine properties of positive solutions of the third order differential equation with advanced argument in neutral term of the form $$(a(t)(b(t)(z'(t))^{\alpha})')'+q(t)y^{\alpha}(t)=0,$$(a(t)(b(t)(z′(t))α)′)′+q(t)yα(t)=0,where $${z(t)=y(t)+p(t)y(\sigma(t))}$$z(t)=y(t)+p(t)y(σ(t)) . They show that the positive solutions… Click to show full abstract
AbstractWe examine properties of positive solutions of the third order differential equation with advanced argument in neutral term of the form $$(a(t)(b(t)(z'(t))^{\alpha})')'+q(t)y^{\alpha}(t)=0,$$(a(t)(b(t)(z′(t))α)′)′+q(t)yα(t)=0,where $${z(t)=y(t)+p(t)y(\sigma(t))}$$z(t)=y(t)+p(t)y(σ(t)) . They show that the positive solutions are in fact Kneser type solutions and then provide lower and upper estimate that yield the rate of convergence to zero for such solutions. An example is provided to illustrate the importance of the main result.
Journal Title: Acta Mathematica Hungarica
Year Published: 2017
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