Decaying positive global solutions of second order difference equations with mean curvature operator
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A boundary value problem on an unbounded domain, associated to difference equations with the Euclidean mean curvature operator is considered. The existence of solutions which are positive on the whole domain and decaying at infinity is examined by proving new Sturm comparison theorems for linear difference equations and using a fixed point approach based on a linearization device. The process of discretization of the boundary value problem on the unbounded domain is examined, and some discrepancies between the discrete and the continuous cases are pointed out, too.
Keywordssecond order nonlinear difference equations, Euclidean mean curvature operator, boundary value problems, decaying solutions, recessive solutions, comparison theorems
Document typePeer reviewed
Document versionFinal PDF
SourceElectronic Journal of Qualitative Theory of Differential Equations. 2020, vol. 2020, issue 72, p. 1-16.
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