Degree theories and invariance of domain for perturbed maximal monotone operators in Banach spaces. (English) Zbl 1160.47044

This paper is devoted to the extension of the invariance of domain theorem to different kinds of perturbations of a maximal monotone operator \(T:X\supset D(T)\to 2^{X^*}\), where \(X\) is a real reflexive Banach space with dual \(X^*\). Namely, the authors develop an invariance of domain theory for operators of the form \[ T+C:D(T)\cap D(C)\to 2^{X^*} \] under several conditions for the operators \(T\) and \(C:X\supset D(C)\to X^*\).


47H14 Perturbations of nonlinear operators
47H07 Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces
47H11 Degree theory for nonlinear operators