An Enclosing Theorem and a Monotone Iterative Scheme for Elliptic Systems Having Nonmonotone Nonlinearities
Siegfried Carl · ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik · 1990
Abstract This paper presents an existence and enclosure result for solutions of semilinear elliptic systems in case that the nonlinearities do not possess any monotonicity properties. Moreover, it is shown that even in this case one is able to establish a monotone iterative scheme for constructing the solution, provided that a certain matrix, which is related to the spectrum of an associated linear differential operator, is positive definite.