The existence of solutions to a Volterra integral equation
Annales Polonici Mathematici (1996)
- Volume: 64, Issue: 2, page 175-182
- ISSN: 0066-2216
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topWojciech Mydlarczyk. "The existence of solutions to a Volterra integral equation." Annales Polonici Mathematici 64.2 (1996): 175-182. <http://eudml.org/doc/269967>.
@article{WojciechMydlarczyk1996,
abstract = {We study the equation u = k∗g(u) with k such that ln k is convex or concave and g is monotonic. Some necessary and sufficient conditions for the existence of nontrivial continuous solutions u of this equation are given.},
author = {Wojciech Mydlarczyk},
journal = {Annales Polonici Mathematici},
keywords = {the Volterra convolution type integral equations; Volterra integral equation; uniqueness; existence; nontrivial solutions},
language = {eng},
number = {2},
pages = {175-182},
title = {The existence of solutions to a Volterra integral equation},
url = {http://eudml.org/doc/269967},
volume = {64},
year = {1996},
}
TY - JOUR
AU - Wojciech Mydlarczyk
TI - The existence of solutions to a Volterra integral equation
JO - Annales Polonici Mathematici
PY - 1996
VL - 64
IS - 2
SP - 175
EP - 182
AB - We study the equation u = k∗g(u) with k such that ln k is convex or concave and g is monotonic. Some necessary and sufficient conditions for the existence of nontrivial continuous solutions u of this equation are given.
LA - eng
KW - the Volterra convolution type integral equations; Volterra integral equation; uniqueness; existence; nontrivial solutions
UR - http://eudml.org/doc/269967
ER -
References
top- [1] G. Gripenberg, On the uniqueness of solutions of Volterra equations, J. Integral Equations Appl. 2 (1990), 421-430. Zbl0826.45002
- [2] R. K. Miller, Nonlinear Volterra Integral Equations, W. A. Benjamin, Menlo Park, Calif., 1971.
- [3] W. Mydlarczyk, The existence of nontrivial solutions of Volterra equations, Math. Scand. 68 (1991), 83-88. Zbl0701.45002
- [4] W. Mydlarczyk, Remarks on a nonlinear Volterra equation, Ann. Polon. Math. 53 (1991), 227-232. Zbl0724.45005
- [5] W. Okrasiński, Nontrivial solutions to nonlinear Volterra integral equations, SIAM J. Math. Anal. 4 (1991), 1007-1015. Zbl0735.45005
- [6] W. Okrasiński, On a nonlinear Volterra integral equation, Math. Methods Appl. Sci. 8 (1986), 345-350. Zbl0603.45008
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