Regularly varying solutions of half-linear differential equations with retarded and advanced arguments

Rok, strany: 2015, 1361 - 1402

Sharp conditions are established for the existence of slowly varying solution and regularly varying solution of index $1$ of the half-linear functional differential equation with both retarded and advanced arguments of the form

$$ (|x'(t)|^α sgn x'(t))'\pm p(t)|x(g(t))|^α sgn x(g(t))\pm q(t)|x(h(t))|^α sgn x(h(t))=0, $$

where $α>0$ is a constant, $p,q:[a,∞)\to (0,∞)$, $a\geqq 0$ are continuous functions, $g$, $h$ are continuous and increasing with $g(t)t$ for $t≥ a$ and $\lim_t\to∞ g(t)=\nb ∞$.

ISO 690:

Manojlović, J., Tanigawa, T. 2015. Regularly varying solutions of half-linear differential equations with retarded and advanced arguments. In Mathematica Slovaca, vol. 65, no.6, pp. 1361-1402. 0139-9918. DOI: https://doi.org/10.1515/ms-2015-0095

APA:

Manojlović, J., Tanigawa, T. (2015). Regularly varying solutions of half-linear differential equations with retarded and advanced arguments. Mathematica Slovaca, 65(6), 1361-1402. 0139-9918. DOI: https://doi.org/10.1515/ms-2015-0095