On solvability of functional equations in the space of continuous vector functions. (English) Zbl 0866.47044

Kiguradze, I.

Mem. Differ. Equ. Math. Phys. 6, 109-112 (1995).

We establish sufficient conditions for solvability of the functional equation \[ x(t)=p(x)(t)+q(x)(t),\tag{1} \] where \(p:C([a,b];\mathbb{R}^n)\to C([a,b]; \mathbb{R}^n)\) and \(q:C([a,b];\mathbb{R}^n)\to C([a,b];\mathbb{R}^n)\) are, respectively, linear and nonlinear operators.

MSC:

47J05

Equations involving nonlinear operators (general)

Keywords:

space of continuous vector functions; solvability; functional equation; nonlinear operators