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A nonlinear Abel equation on the whole line. (English) Zbl 0993.45006
The author investigates some properties of the solutions of the Volterra integral equation $$u(x)=\int_{-\infty}^{x}(x-s)^{\alpha-1}g(u(s)) ds\quad (-\infty<x,\ 0<\alpha<1),$$ where $g:[0,\infty)\rightarrow [0,\infty)$ is continuous and nondecreasing with $g(0)=0$ and $g(x)>0$ for $x>0$.

45G05Singular nonlinear integral equations
Full Text: DOI
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[2] Bushell, P. J.; Okrasiński, W.: Uniqueness for a class of non-linear Volterra integral equations with convolution kernel. Math. proc. Camb. philos. Soc. 106, 547-552 (1989) · Zbl 0689.45013
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[9] Roberts, C. A.; Lasseigne, D. G.; Olmstead, W. E.: Volterra equations which model explosion in a diffusive medium. J. integral equations appl. 5, 531-546 (1993) · Zbl 0804.45002