International Journal of Mathematics and Mathematical Sciences
Volume 24 (2000), Issue 6, Pages 389-401
doi:10.1155/S0161171200002362

Decomposition conditions for two-point boundary value problems

Abstract

We study the solvability of the equation x″=f(t,x,x′) subject to Dirichlet, Neumann, periodic, and antiperiodic boundary conditions. Under the assumption that f can be suitably decomposed, we prove approximation solvability results for the above equation by applying the abstract continuation type theorem of Petryshyn on A-proper mappings.