Differential and Integral Equations

Positive homoclinic solutions for the discrete $p$-Laplacian with a coercive weight function

Antonio Iannizzotto and Vicenţiu D. Rădulescu

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Abstract

We study a $p$-Laplacian difference equation on the set of integers, involving a coercive weight function and a reaction term satisfying the Ambrosetti--Rabinowitz condition. By means of critical-point theory and a discrete maximum principle, we prove the existence of a positive homoclinic solution.

Article information

Source
Differential Integral Equations, Volume 27, Number 1/2 (2014), 35-44.

Dates
First available in Project Euclid: 12 November 2013

Permanent link to this document
https://projecteuclid.org/euclid.die/1384282852

Mathematical Reviews number (MathSciNet)
MR3161594

Zentralblatt MATH identifier
1313.39004

Subjects
Primary: 39A10: Difference equations, additive 47J30: Variational methods [See also 58Exx]

Citation

Iannizzotto, Antonio; Rădulescu, Vicenţiu D. Positive homoclinic solutions for the discrete $p$-Laplacian with a coercive weight function. Differential Integral Equations 27 (2014), no. 1/2, 35--44. https://projecteuclid.org/euclid.die/1384282852


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