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Keywords:
first order equation; differential equation with deviating arguments; initial value problems
first order equation; differential equation with deviating arguments; initial value problems
Summary:
Conditions for the existence and uniqueness of a solution of the Cauchy problem \[ u^{\prime }(t)=p(t)u(\tau (t))+q(t)\,,\qquad u(a)=c\,, \] established in [2], are formulated more precisely and refined for the special case, where the function $\tau $ maps the interval $]a,b[$ into some subinterval $[\tau _0,\tau _1]\subseteq [a,b]$, which can be degenerated to a point.
References:
[1] Bravyi E.: A note on the Fredholm property of boundary value problems for linear functional differential equations. Mem. Differential Equations Math. Phys. 20 (2000), 133–135. MR 1789344 | Zbl 0968.34049
[2] Bravyi E., Hakl R., Lomtatidze A.: Optimal conditions for unique solvability of the Cauchy problem for first order linear functional differential equations. Czechoslovak Math. J., to appear. MR 1923257 | Zbl 1023.34055
[3] Hakl R., Lomtatidze A., Půža B.: New optimal conditions for unique solvability of the Cauchy problem for first order linear functional differential equations. Math. Bohem., to appear. MR 1942637 | Zbl 1017.34065
[4] Kiguradze I., Půža B.: On boundary value problems for systems of linear functional differential equations. Czechoslovak Math. J. 47 (1997), No. 2, 341–373. MR 1452425 | Zbl 0930.34047
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