Hiroyuki Usami and Takuro Yoshimi

Existence of Solutions of Integral Equations Related to Inverse Problems of Quasilinear Ordinary Differential Equations

abstract:
We consider nonlinear integral equations related to inverse problems for quasilinear ordinary differential equations. We establish a global existence of solutions for them by means of the method of successive approximations and fractional calculus. Our results give a generalization of the recent result in [Global existence of a restoring force realizing a prescribed half-period. J. Differential Equations 248 (2010), No. 10, 2562-2584.].

Mathematics Subject Classification: 34A55, 45G05

Key words and phrases: Inverse problem, nonlinear integral equation, fractional calculus