Geodesic
On the existence and uniqueness of solution of the Cauchy problem for linear integro-differential equations with operator coefficients
Applications of Mathematics, Tome 16 (1971) no. 1, pp. 64-80.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

In the theory of neutron fields some problems arise, which may be described by means of integro-differential equations with initial conditions. The aim of the paper is to state a class of problems covering this physical example and to prove the existence, uniqueness and continuous dependence of their solutions on the given data. A variational approach, presented in a previous author's article, is used to establish the definition of generalized (weak) solutions of the Cauchy problem, which is an extension of the concept of generalized solutions of differential equations.
DOI : 10.21136/AM.1971.103326
Classification : 45J05, 47G05 
@article{10_21136_AM_1971_103326,
     author = {Hlav\'a\v{c}ek, Ivan},
     title = {On the existence and uniqueness of solution of the {Cauchy} problem for linear integro-differential equations with operator coefficients},
     journal = {Applications of Mathematics},
     pages = {64--80},
     publisher = {mathdoc},
     volume = {16},
     number = {1},
     year = {1971},
     doi = {10.21136/AM.1971.103326},
     mrnumber = {0300158},
     zbl = {0217.15801},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.1971.103326/}
}
TY  - JOUR
AU  - Hlaváček, Ivan
TI  - On the existence and uniqueness of solution of the Cauchy problem for linear integro-differential equations with operator coefficients
JO  - Applications of Mathematics
PY  - 1971
SP  - 64
EP  - 80
VL  - 16
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.21136/AM.1971.103326/
DO  - 10.21136/AM.1971.103326
LA  - en
ID  - 10_21136_AM_1971_103326
ER  - 
%0 Journal Article
%A Hlaváček, Ivan
%T On the existence and uniqueness of solution of the Cauchy problem for linear integro-differential equations with operator coefficients
%J Applications of Mathematics
%D 1971
%P 64-80
%V 16
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.21136/AM.1971.103326/
%R 10.21136/AM.1971.103326
%G en
%F 10_21136_AM_1971_103326
Hlaváček, Ivan. On the existence and uniqueness of solution of the Cauchy problem for linear integro-differential equations with operator coefficients. Applications of Mathematics, Tome 16 (1971) no. 1, pp. 64-80. doi : 10.21136/AM.1971.103326. http://geodesic.mathdoc.fr/articles/10.21136/AM.1971.103326/

Cité par Sources :