We consider a difference equation involving the discrete p-Laplacian operator, depending on a positive real parameter l. We prove, under convenient assumptions, that for l big enough the equations admit at least one homoclinic constant sign solution in Z. Our method consists in two parts: first, we prove the existence of two Dirichlet-type solutions for the equation in the discrete interval [-n,n], for all n big enough; then, we show that such solutions converge to a homoclinic solution in Z, as n tends to infinity.

Existence of homoclinic constant sign solutions for a difference equation on the integers

IANNIZZOTTO, ANTONIO
2013-01-01

Abstract

We consider a difference equation involving the discrete p-Laplacian operator, depending on a positive real parameter l. We prove, under convenient assumptions, that for l big enough the equations admit at least one homoclinic constant sign solution in Z. Our method consists in two parts: first, we prove the existence of two Dirichlet-type solutions for the equation in the discrete interval [-n,n], for all n big enough; then, we show that such solutions converge to a homoclinic solution in Z, as n tends to infinity.
2013
Difference equations; Discrete p-Laplacian
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11562/765761
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