Nonlinear boundary value problems and operators |
| |
Authors: | R. Kannan John Locker |
| |
Affiliation: | Department of Mathematics, University of Missouri, St. Louis, Missouri 63121 USA;Department of Mathematics, Colorado State University, Fort Collins, Colorado 80523 USA |
| |
Abstract: | We consider nonlinear boundary value problems of the type for the existence of solutions. It is assumed that L is a 2nth-order linear differential operator in the real Hilbert space S = L2[a, b] which admits a decomposition of the form where T is an nth-order linear differential operator and N is a nonlinear operator defined on a subspace of S. The decomposition of L induces a natural decomposition of the generalized inverse of L. Using the method of “alternative problems,” we split the boundary value problem into an equivalent system of two equations. The theory of monotone operators and the theory of nonlinear Hammerstein equations are then utilized to consider the solvability of the equivalent system. |
| |
Keywords: | |
本文献已被 ScienceDirect 等数据库收录! |
|