Three positive solutions for a nonlinear partial discrete Dirichlet problem with ( p , q ) $(p,q)$ -Laplacian operator

Abstract In this paper, we prove the existence of three solutions to a partial difference equation with ( p , q ) $(p,q)$ -Laplacian operator by using critical point theory. Furthermore, based on the strong maximum principle, we prove that the three solutions are positive under appropriate nonlinear...

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Bibliographic Details
Published in:Boundary Value Problems
Main Authors: Feng Xiong, Zhan Zhou
Format: Article
Language:English
Published: SpringerOpen 2022-02-01
Subjects:
Boundary value problem
Three positive solutions
Partial difference equation
( p , q ) $(p,q)$ -Laplacian
Critical point theory
Online Access:https://doi.org/10.1186/s13661-022-01588-z
Description
Summary:Abstract In this paper, we prove the existence of three solutions to a partial difference equation with ( p , q ) $(p,q)$ -Laplacian operator by using critical point theory. Furthermore, based on the strong maximum principle, we prove that the three solutions are positive under appropriate nonlinearity assumptions. Finally, we also give an example to illustrate our main results.
ISSN:1687-2770

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