Existence and multiplicity results for first-order Stieltjes differential equations

Abstract

In this article, we establish existence and multiplicity results for first-order Stieltjes differential equations satisfying a periodic boundary condition or an initial value condition. No monotonicity condition involving the right-hand side ff is imposed at the discontinuity points of the derivator gg. Our results rely on the fixed point index theory and new notions of strict lower and upper solutions. An application to a population model with an extreme event is presented to study the persistence of a species.

Keywords

• stieltjes differential equations
• periodic boundary conditions
• initial value problems
• lower and upper solutions
• strict lower and upper solutions
• multiple solutions
• primary 34a06
• secondary 34b15
• 34b60
• 34a36