# Positive solutions of a renewal equation

Annales Polonici Mathematici (1992)

- Volume: 57, Issue: 1, page 91-97
- ISSN: 0066-2216

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topJanusz Traple. "Positive solutions of a renewal equation." Annales Polonici Mathematici 57.1 (1992): 91-97. <http://eudml.org/doc/262384>.

@article{JanuszTraple1992,

abstract = {An existence theorem is proved for the scalar convolution type integral equation $x(t) = ∫_\{-∞\}^\{∞\} h(t - s)f(s,x(s))ds$.},

author = {Janusz Traple},

journal = {Annales Polonici Mathematici},

keywords = {integral equations; convolution; renewal integral equations; positive solutions; convolution type integral equation; population dynamics; positive periodic solution; convolution inequalities},

language = {eng},

number = {1},

pages = {91-97},

title = {Positive solutions of a renewal equation},

url = {http://eudml.org/doc/262384},

volume = {57},

year = {1992},

}

TY - JOUR

AU - Janusz Traple

TI - Positive solutions of a renewal equation

JO - Annales Polonici Mathematici

PY - 1992

VL - 57

IS - 1

SP - 91

EP - 97

AB - An existence theorem is proved for the scalar convolution type integral equation $x(t) = ∫_{-∞}^{∞} h(t - s)f(s,x(s))ds$.

LA - eng

KW - integral equations; convolution; renewal integral equations; positive solutions; convolution type integral equation; population dynamics; positive periodic solution; convolution inequalities

UR - http://eudml.org/doc/262384

ER -

## References

top- [1] K. L. Cooke and J. L. Kaplan, A periodicity threshold theorem for epidemics and population growth, Math. Biosci. 31 (1976), 87-104. Zbl0341.92012
- [2] P. Kasprowski, On positive solutions of nonlinear convolution equations, unpublished paper. Zbl0547.28010
- [3] W. P. London and J. A. Yorke, Recurrent outbreaks of measles, chickenpox and mumps. II. Systematic differences in contact rates and stochastic effects, Amer. J. Epidemiol. 98 (1973), 469-482.
- [4] K. E. Swick, A model of single species population growth, SIAM J. Math. Anal. 7 (1976), 565-576. Zbl0343.92011

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