Nonlocal difference equations with sign-changing coefficients

• Published in: Applied mathematics letters Vol. 106; p. 106371
• Main Authors: Goodrich, Christopher S., Lyons, Benjamin
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.08.2020
• Subjects: Coercivity; Jensen’s inequality; Nonlocal difference equation; Positive solution; Sign-changing coefficient; Jensen’s inequality; Sign-changing coefficient; Nonlocal difference equation; Coercivity; Positive solution

We consider second-order difference equations of the form −A∑j=1Nαj(utj)qΔ2u(n)=λf(n,u(n+1))subject to the Dirichlet boundary conditions u(0)=0=u(b+2). We demonstrate that using a nonstandard cone and associated open set can allow one to deduce the existence of at least one positive solution even in...