# The existence of solutions to a Volterra integral equation

Annales Polonici Mathematici (1996)

- Volume: 64, Issue: 2, page 175-182
- ISSN: 0066-2216

## Access Full Article

top## Abstract

top## How to cite

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

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.