Solutions with a prescribed interval of positivity for differential systems with nonlocal conditions

摘要

Based on fixed point index, the paper develops a theory of existence, localization and multiplicity of solutions to first-order differential systems subject to linear nonlocal conditions. The main features concern the role of the support of the nonlocal condition and the positivity of solutions which is only required on a prescribed subinterval. Several examples of problems admitting at least one, two, or sequences of such solutions are included, and numerical solutions are obtained using the Mathematica shooting program with starting initial conditions suggested by the theoretical localization results.