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A note on a Volterra integral equation. (English) Zbl 1038.45004

This short note tries to establish the existence of nontrivial solutions of the nonlinear Volterra integral equation \[ u(t) = \int_0^x (x-s)^{\alpha - 1} g(u(s))ds, \quad x > 0, \] where \(\alpha > 0\), \(g(0) = 0\), and \(g(r) \geq 0\) for \(r > 0\). It cites only two papers, namely W. Mydlarczyk [J. Math. Scand. 68, 83–88 (1991; Zbl 0701.45002), and J. Math. Anal. Appl. 181, 248–253 (1994; Zbl 0808.45008)], and it claims that some of the results in these papers can be extended.

MSC:

45G05 Singular nonlinear integral equations
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