Multiple solutions of
nonlinear boundary value problems for two-dimensional differential
Abstract: This paper discusses the quasilinearization process, that is, reduction of a given boundary value problem to a quasi-linear one. Quasi-linear BVP has a solution of definite type which is induced by oscillatory properties of the linear part of a system. Conditions are given for a solution of a modified (quasi-linear) BVP to satisfy also the original problem. It is shown that multiple quasilinearizations with different linear parts if possible lead to multiple solutions.
Keywords: Boundary value problem, quasi-linear equation, multiple solutions
Received: July 2008; Revised: March 2009; Published: September 2009.