A criterion for isolated solution structure and global computability for operator equations

This paper considers the description and determination of the fixed points of compact, continuously differentiable mappings T in Banach spaces. In particular, our results describe situations when the fixed point set of T is isolated, and when at least one fixed point can be computed by a globally convergent Newton/continuation algorithm, beginning at zero. The entire framework is motivated by applications to nonlinear elliptic systems for which these properties hold.