非线性Volterra-Stieltjes积分方程的解

Solvability of nonlinear Volterra-Stieltjes integral equation

利用Schauder不动点定理和饱和解的理论,研究下列非线性Volterra- Stieltjes积分方程x(t)=h(t)+∫_0~t u(t,s,x(s))d_sg(t,s).在适当的条件下,证明了上述方程在[0,+∞)上有连续解.

By using Schauder fixed point theorem and the theory of saturated solution the nonlinear Volterra-Stieltjes integral equation x(t)= h(t)+∫_0~t u(t,s,x(s))d_sg(t,s) is studied.It is proved that the equation has a solution x(t)∈[0,+∞) under some appropriate conditions.