Nontrivial solutions for a class of nonlinear Volterra equations with convolution kernel. (English) Zbl 0745.45001
The author studies Volterra integral equations of the form \(u(x)=\int^ x_ 0k(x-s)g(u(s))ds\) for \(x\geq 0\), where \(k\geq 0\) is an integrable function and \(g\) is an increasing absolutely continuous function with \(g(0)=0\). Sufficient conditions and necessary conditions for the existence of a positive nontrivial solution are obtained. An example is given.
Reviewer: W.Petry (Düsseldorf)
MSC:
45G10 | Other nonlinear integral equations |
45M20 | Positive solutions of integral equations |
45D05 | Volterra integral equations |