Let Λ be a linear differential operator on (a, b) of order 2m with leading coefficient possessing an integrable reciprocal. Global Cm‐1(a, b) solutions are shown to exist for certain nonlinear multipoint boundary value problems of the form A u = F(u, …, um‐1, where linear combinations of derivatives through order m – 1 are specified at points interior to (a, b). The associated linear problem is completely solved through the construction of an appropriate Green's function which determines a compact operator G = A−1. The linear eigenvalue problem is examined and a complete orthonormal system exhibited in L2(a, b). Solutions of the nonlinear problem are obtained by exhibiting fixed points for the operator GF.
|Original language||English (US)|
|Number of pages||8|
|Journal||ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik|
|State||Published - Jan 1 1973|
ASJC Scopus subject areas
- Computational Mechanics
- Applied Mathematics