On the eigenvalue problem for perturbed nonlinear maximal monotone operators in reflexive Banach spaces

摘要

Let X be a real reflexive Banach space with dual X* and G subset of X open and bounded and such that 0 is an element of G. Let T : X superset of D(T). 2(X*) be maximal monotone with 0 is an element of D(T) and 0 is an element of T(0), and C : X superset of D(C) -> X* with 0 is an element of D(C) and C(0) not equal 0. A general and more unified eigenvalue theory is developed for the pair of operators (T, C). Further conditions are given for the existence of a pair (lambda, x). (0,8) x (D( T + C) n boolean AND partial derivative G) such that