Duality for Stieltjes differential and integral equations

Abstract

We propose new definitions of adjoint equations to first-order linear Stieltjes differential and integral equations. We investigate the existence and uniqueness of their solutions, provide explicit solution formulas, and obtain corresponding versions of Lagrange's identity.

We show that our results are compatible with known results for dynamic equations on time scales, which are included as aspecial case. (c) 2022 Elsevier Inc. All rights reserved.

Keywords

• adjoint equation
• Lagrange's identity
• Stieltjes differential equation
• generalized ordinary differential equation
• Volterra-Stieltjes integral equation
• dynamic equation