Geodesic
Asymptotic behaviour of solutions of some linear delay differential equations
Mathematica Bohemica, Tome 125 (2000) no. 3, pp. 355-364

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In this paper we investigate the asymptotic properties of all solutions of the delay differential equation y'(x)=a(x)y(\tau(x))+b(x)y(x),\qquad x\in I=[x_0,\infty). We set up conditions under which every solution of this equation can be represented in terms of a solution of the differential equation z'(x)=b(x)z(x),\qquad x\in I and a solution of the functional equation |a(x)|\varphi(\tau(x))=|b(x)|\varphi(x),\qquad x\in I.
In this paper we investigate the asymptotic properties of all solutions of the delay differential equation y'(x)=a(x)y(\tau(x))+b(x)y(x),\qquad x\in I=[x_0,\infty). We set up conditions under which every solution of this equation can be represented in terms of a solution of the differential equation z'(x)=b(x)z(x),\qquad x\in I and a solution of the functional equation |a(x)|\varphi(\tau(x))=|b(x)|\varphi(x),\qquad x\in I.
DOI : 10.21136/MB.2000.126125
Classification : 34K15, 34K25, 39B05, 39B22, 39B99
Keywords: asymptotic behaviour; differential equation; delayed argument; functional equation 
Čermák, Jan. Asymptotic behaviour of solutions of some linear delay differential equations. Mathematica Bohemica, Tome 125 (2000) no. 3, pp. 355-364. doi: 10.21136/MB.2000.126125
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