Linear Integral Equations of Volterra Concerning Henstock Integrals

Federson, M.; Bianconi, R.

Real Anal. Exchange, Tome 25 (1999) no. 1, p. 389-418 / Harvested from Project Euclid

Résumé

We establish conditions for the existence of solutions of the linear integral equation of Volterra \begin{equation} x\left( t\right) +^{\ast }\int\nolimits_{[ a,t] }\alpha ( s) x ( s )\, ds=f ( t ) ,\quad t\in [ a,b ] ,\tag{$V_{\ast}$} \end{equation} where the functions are Banach space-valued and $^{\ast }\int $ denotes either the Bochner-Lebesgue or the Henstock integral. In some cases it is possible to calculate the solution of $( V)_{\ast }$ explicitly. We give several examples.

Publié le : 1999-05-15
Classification: Volterra, Henstock integral, Bochner integral, integral equation, 45D05, 34A12, 26A39

@article{1231187614,
     author = {Federson, M. and Bianconi, R.},
     title = {Linear Integral Equations of Volterra Concerning Henstock Integrals},
     journal = {Real Anal. Exchange},
     volume = {25},
     number = {1},
     year = {1999},
     pages = { 389-418},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1231187614}
}

Federson, M.; Bianconi, R. Linear Integral Equations of Volterra Concerning Henstock Integrals. Real Anal. Exchange, Tome 25 (1999) no. 1, pp.  389-418. http://gdmltest.u-ga.fr/item/1231187614/