Boundary and periodic value problems for systems of differential equations under Bernstein-Nagumo growth condition

Abstract

In this paper, we establish some existence results for boundary and periodic value problems for systems of nonlinear differential equations with right-hand side satisfying a Berntein-Nagumo growth condition. Hartman's condition ($|f| \le 2k(\langle x,f\rangle + |x'|^2) + K$) is not assumed. This assumption is replaced by one which is automatically satisfied in the scalar case.