Unique solvability of nonlinear Volterra equations in weighted spaces (Q1197404)

The classical tools are used in order to obtain existence and uniqueness results for a nonlinear integral equation of the type \(x(t)=g(t)+\int_ IF(t,s,x(s))ds\) \((I\) is an interval, possibly unbounded) or \(x(t)=g(t)+\int^ t_{-\infty}F(t,s,x(s))ds\). The considerations are placed in weighted function spaces \(C(I,w)\) \((w\) is a continuous and positive weight function on \(I)\) or \(L^ p(I,w)\) (in this case \(w\) is positive and measurable).