Nonlocal difference equations with sign-changing coefficients

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...

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Bibliographic Details
Published inApplied mathematics letters Vol. 106; p. 106371
Main Authors Goodrich, Christopher S., Lyons, Benjamin
Format Journal Article
LanguageEnglish
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
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Summary: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 the case where the function A may change sign. Jensen’s inequality plays an important role in our analysis.
ISSN:0893-9659
1873-5452
DOI:10.1016/j.aml.2020.106371