Improved oscillation results for second-order half-linear delay differential equations

Authors : George E. CHATZARAKİS, İrena JADLOVSKA

Pages : 170-179

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Publication Date : 2019-02-01

Article Type : Research Paper

Abstract : In  this paper,  we study the second-order half-linear delay differential equation of the form \[insert ignore into journalissuearticles values(rinsert ignore into journalissuearticles values(t);insert ignore into journalissuearticles values(y`insert ignore into journalissuearticles values(t););^\alpha);`+qinsert ignore into journalissuearticles values(t);y^\alphainsert ignore into journalissuearticles values(\tauinsert ignore into journalissuearticles values(t););= 0.\:\:\:insert ignore into journalissuearticles values(E);\] We establish new oscillation criteria for insert ignore into journalissuearticles values(E);, which   improve a number of related ones in the literature. Our approach  essentially involves  establishing sharper estimates for the positive solutions of insert ignore into journalissuearticles values(E); than those presented in known works and a comparison principle with first-order delay differential inequalities.   We illustrate the improvement over the known results by applying and comparing our method with the other known methods on the particular example of Euler-type equations.
Keywords : half linear differential equation, delay, second order, oscillation