Properties of solutions of a heterogeneous differential equation of the second order

dc.contributor.authorMulyava, Oksana
dc.contributor.authorSheremeta, Miroslav
dc.contributor.authorTrukhan, Yu. S.
dc.date.accessioned2022-02-07T20:59:32Z
dc.date.available2022-02-07T20:59:32Z
dc.date.issued2019
dc.description.abstractSuppose that a power seriesA(z) =∑∞n=0anznhas the radius of convergenceR[A]∈[1,+∞].For a heterogeneous differential equationz2w′′+ (β0z2+β1z)w′+ (γ0z2+γ1z+γ2)w=A(z)with complex parameters geometrical properties of its solutions (convexity, starlikeness and close-to-convexity) in the unit disk are investigated. Two cases are considered: ifγ26=0 andγ2=0. Wealso consider cases when parameters of the equation are realnumbers. Also we prove that for asolutionfof this equation the radius of convergenceR[f]equals toR[A]and the recurrent formulasfor the coefficients of the power series off(z)are found. For entire solutions it is proved that theorder of a solutionfis not less then the order ofA(̺[f]≥̺[A]) and the estimate is sharp. The sameinequality holds for generalized orders (̺αβ[f]≥̺αβ[A]). For entire solutions of this equation thebelonging to convergence classes is studied. Finally, we consider a linear differential equation of theendless order∞∑n=0ann!w(n)=Φ(z), and study a possible growth of its solutions.uk_UA
dc.identifier.citationMulyava, O. Properties of solutions of a heterogeneous differential equation of the second order / O. Mulyava, M. Sheremeta, Yu. Trukhan // Carpathian Mathematical Publications. – 2019. – Vol. 11, Issue 2. – P. 379–398.uk_UA
dc.identifier.urihttps://dspace.nuft.edu.ua/handle/123456789/37065
dc.language.isoenuk_UA
dc.subjectdifferential equationuk_UA
dc.subjectconvexityuk_UA
dc.subjectstarlikenessuk_UA
dc.subjectclose-to-convexityuk_UA
dc.subjectgeneralized orderuk_UA
dc.subjectconvergence classuk_UA
dc.subjectдиференціальне рівнянняuk_UA
dc.subjectопуклістьuk_UA
dc.subjectзіркоподібністьuk_UA
dc.subjectблизька до опуклостіuk_UA
dc.subjectузагальнений порядокuk_UA
dc.subjectклас збіжностіuk_UA
dc.subjectкафедра вищої математики імені проф. Можара В. І.uk_UA
dc.titleProperties of solutions of a heterogeneous differential equation of the second orderuk_UA
dc.typeArticleuk_UA

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