Some Remarks on the Continuation Method of Leray-Schauder-Rabinowitz and the Method of Monotone Iterations.

摘要

Certain physical phenomena can be modelled by the nonlinear eigenvalue problem (P). Under minimal assumptions on the nonlinear term, which may be of interest in some applications, the existence of solutions can be obtained by several known methods. The purpose of this paper is to compare two such methods, namely the continuation method due to Leray and Schauder as extended by Rabinowitz, and the method of monotone iterations. Our results are then applied to problem (P).