On the Aronszajn property for integral equations in Banach space
- Volume: 83, Issue: 1, page 93-99
- ISSN: 1120-6330
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topSzufla, Stanisław. "On the Aronszajn property for integral equations in Banach space." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 83.1 (1989): 93-99. <http://eudml.org/doc/287520>.
@article{Szufla1989,
abstract = {For the integral equation (1) below we prove the existence on an interval $J = [0, a]$ of a solution $x$ with values in a Banach space $E$, belonging to the class $L^\{p\}(J,E)$, $p>1$. Further, the set of solutions is shown to be a compact one in the sense of Aronszajn.},
author = {Szufla, Stanisław},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Integral equations; Banach spaces; Aronszajn property; Banach space; existence; compact absolute retracts},
language = {eng},
month = {12},
number = {1},
pages = {93-99},
publisher = {Accademia Nazionale dei Lincei},
title = {On the Aronszajn property for integral equations in Banach space},
url = {http://eudml.org/doc/287520},
volume = {83},
year = {1989},
}
TY - JOUR
AU - Szufla, Stanisław
TI - On the Aronszajn property for integral equations in Banach space
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1989/12//
PB - Accademia Nazionale dei Lincei
VL - 83
IS - 1
SP - 93
EP - 99
AB - For the integral equation (1) below we prove the existence on an interval $J = [0, a]$ of a solution $x$ with values in a Banach space $E$, belonging to the class $L^{p}(J,E)$, $p>1$. Further, the set of solutions is shown to be a compact one in the sense of Aronszajn.
LA - eng
KW - Integral equations; Banach spaces; Aronszajn property; Banach space; existence; compact absolute retracts
UR - http://eudml.org/doc/287520
ER -
References
top- ARONSZAJN, N., 1942. Le correspondant topologique de l'unicité dans la théorie des équations différentielles. Ann. of Math., 43: 730-738. Zbl0061.17106MR7195
- BROWDER, F.E. and GUPTA, C.P., 1969. Topological degree and nonlinear mappings of analytical type in Banach space. J. Math. Anal. Appl., 26: 390-402. Zbl0176.45401MR257826
- DEIMLING, K., 1977. Ordinary differential equations in Banach spaces. Lect. Notes Math., 596: Springer Verlag. Zbl0361.34050MR463601
- LAKSHMIKANTHAM, V. and LEELA, S., 1981. Nonlinear differential equations in abstract spaces. Pergamon Press. Zbl0456.34002MR616449
- MARTIN, R.H., 1976. Nonlinear operators and differential equations in Banach spaces. Wiley, New York. Zbl0333.47023MR492671
- MÖNCH, H., 1980. Boundary value problems for nonlinear ordinary differential equations of second order in Banach space. Nonlinear Analysis, 4: 985-999. Zbl0462.34041MR586861DOI10.1016/0362-546X(80)90010-3
- ORLICZ, W. and SZUFLA, S., 1982. On some classes of nonlinear Volterra integral equations in Banach spaces. Bull. Acad. Polon. Sci. Math., 30: 239-250. Zbl0501.45013MR673260
- SADOVSKII, B.N., 1972. Limit-compact and condensing operators. Russian Mah. Surveys, 27: 85-155. Zbl0243.47033MR428132
- SZUFLA, S., 1982. On the existence of solutions of differential equations in Banach spaces. Bull. Acad. Polon. Sci. Math., 30: 507-515. Zbl0532.34045MR718727
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