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The existence of nontrivial solutions of Volterra equations. (English) Zbl 0701.45002

The paper is devoted to the study of the equation \(u(x)=\int^{x}_{0}(x-s)^{\alpha -1}g(u(s))ds\quad (x\geq 0,\quad \alpha >0).\) In the case of nondecreasing g such that \(g(x)>0\) for \(x>0\) some necessary and sufficient condition for the existence of nontrivial solutions of this equation is given.
Reviewer: W.Mydlarczyk

MSC:

45G10 Other nonlinear integral equations
45D05 Volterra integral equations
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