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Kusano, Takaŝi; Manojlović, Jelena; Tanigawa, Tomoyuki

Existence of regularly varying solutions with nonzero indices of half-linear differential equations with retarded arguments. (English) Zbl 1189.34121

Comput. Math. Appl. 59, No. 1, 411-425 (2010).
Summary: Sharp conditions are established for the existence of a pair of regularly varying solutions with nonzero indices of half-linear functional differential equations of the type \[ (|x'(t)|^{\alpha}\text{sgn }x'(t))'=q(t)|x(g(t))|^{\alpha}\text{sgn }x(g(t)),~\alpha>0,~g(t)>0,~g(t)<t. \]

Cited in 7 Documents

MSC:

34K05 General theory of functional-differential equations

Keywords:

half-linear differential equation; functional differential equation; regularly varying solution
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\textit{T. Kusano} et al., Comput. Math. Appl. 59, No. 1, 411--425 (2010; Zbl 1189.34121)
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References:

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