# New optimal conditions for unique solvability of the Cauchy problem for first order linear functional differential equations

Robert Hakl; Alexander Lomtatidze; Bedřich Půža

Mathematica Bohemica (2002)

- Volume: 127, Issue: 4, page 509-524
- ISSN: 0862-7959

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topHakl, Robert, Lomtatidze, Alexander, and Půža, Bedřich. "New optimal conditions for unique solvability of the Cauchy problem for first order linear functional differential equations." Mathematica Bohemica 127.4 (2002): 509-524. <http://eudml.org/doc/249031>.

@article{Hakl2002,

abstract = {The nonimprovable sufficient conditions for the unique solvability of the problem \[ u^\{\prime \}(t)=\ell (u)(t)+q(t),\qquad u(a)=c, \]
where $\ell \: C(I;\mathbb \{R\})\rightarrow L(I;\mathbb \{R\})$ is a linear bounded operator, $q\in L(I;\mathbb \{R\})$, $c\in \mathbb \{R\}$, are established which are different from the previous results. More precisely, they are interesting especially in the case where the operator $\ell $ is not of Volterra’s type with respect to the point $a$.},

author = {Hakl, Robert, Lomtatidze, Alexander, Půža, Bedřich},

journal = {Mathematica Bohemica},

keywords = {linear functional differential equations; differential equations with deviating arguments; initial value problems; linear functional-differential equations; differential equations with deviating arguments; initial value problems},

language = {eng},

number = {4},

pages = {509-524},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {New optimal conditions for unique solvability of the Cauchy problem for first order linear functional differential equations},

url = {http://eudml.org/doc/249031},

volume = {127},

year = {2002},

}

TY - JOUR

AU - Hakl, Robert

AU - Lomtatidze, Alexander

AU - Půža, Bedřich

TI - New optimal conditions for unique solvability of the Cauchy problem for first order linear functional differential equations

JO - Mathematica Bohemica

PY - 2002

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 127

IS - 4

SP - 509

EP - 524

AB - The nonimprovable sufficient conditions for the unique solvability of the problem \[ u^{\prime }(t)=\ell (u)(t)+q(t),\qquad u(a)=c, \]
where $\ell \: C(I;\mathbb {R})\rightarrow L(I;\mathbb {R})$ is a linear bounded operator, $q\in L(I;\mathbb {R})$, $c\in \mathbb {R}$, are established which are different from the previous results. More precisely, they are interesting especially in the case where the operator $\ell $ is not of Volterra’s type with respect to the point $a$.

LA - eng

KW - linear functional differential equations; differential equations with deviating arguments; initial value problems; linear functional-differential equations; differential equations with deviating arguments; initial value problems

UR - http://eudml.org/doc/249031

ER -

## References

top- Introduction to the Theory of Functional Differential Equations, Nauka, Moskva, 1991. (Russian) (1991) MR1144998
- Optimal conditions for unique solvability of the Cauchy problem for first order linear functional differential equations, Czechoslovak Math. J (to appear). (to appear) MR1923257
- A note on the Fredholm property of boundary value problems for linear functional differential equations, Mem. Differential Equations Math. Phys. 20 (2000), 133–135. (2000) Zbl0968.34049MR1789344
- On multi-point boundary value problems for systems of functional differential and difference equations, Mem. Differential Equations Math. Phys. 5 (1995), 1–113. (1995) MR1415806
- On boundary value problems for systems of linear functional differential equations, Czechoslovak Math. J. 47 (1997), 341–373. (1997) MR1452425
- Differential and Integral Equations: Boundary Value Problems and Adjoints, Academia, Praha, 1979. (1979) MR0542283

## Citations in EuDML Documents

top- Jiří Šremr, Solvability conditions of the Cauchy problem for two-dimensional systems of linear functional differential equations with monotone operators
- Robert Hakl, Alexander Lomtatidze, A note on the Cauchy problem for first order linear differential equations with a deviating argument
- Eugene Bravyi, On solvability sets of boundary value problems for linear functional differential equations
- Robert Hakl, Alexander Lomtatidze, Jiří Šremr, Solvability of a periodic type boundary value problem for first order scalar functional differential equations
- Robert Hakl, Alexander Lomtatidze, Jiří Šremr, On an antiperiodic type boundary value problem for first order linear functional differential equations

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