Existence and Multiplicity Results for Systems of First-Order Differential Equations via the Method of Solution-Regions

Abstract

In this paper, we establish existence and multiplicity results for systems of first-order differential equations. To this end, we introduce the method of solution-regions. It generalizes the method of upper and lower solutions and the method of solution-tubes. Our results can also be seen as viability results since we obtain solutions remaining in suitable regions. We give conditions insuring the existence of at least three viable solutions of a system of first-order differential equations. Many examples are presented to show that a large variety of sets can be solution-regions.

Keywords

• system of first order differential equations
• multiple solutions
• initial value and periodic boundary value problems
• fixed point index
• solution-region
• upper and lower solutions
• 34b15
• 34a34
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