<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In this paper, we deal with the existence of at least one and of at least two positive solutions as well the uniqueness of a positive solution for an anisotropic discrete non-linear problem involving <italic>p</italic>(<italic>k</italic>)-Laplacian with Dirichlet boundary value conditions. The technical approach for the existence part is based on a local minimum theorem and on a two critical points theorem for differentiable functionals, and for uniqueness part is based on a Lipschitzian continuous condition on the nonlinearity term.</p></abstract>

In this paper, we deal with the existence of at least one and of at least two positive solutions as well the uniqueness of a positive solution for an anisotropic discrete non-linear problem involving p(k)-Laplacian with Dirichlet boundary value conditions. The technical approach for the existence part is based on a local minimum theorem and on a two critical points theorem for differentiable functionals, and for uniqueness part is based on a Lipschitzian continuous condition on the nonlinearity term.

Existence and uniqueness of positive solution for nonlinear difference equations involving <italic>p</italic>(<italic>k</italic>)-Laplacian operator

Sari Agricultural Sciences and Natural Resources University

The Center of Education of Mathematics and Physics

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Existence and uniqueness of positive solution for nonlinear difference equations involving ()-Laplacian operator

In this paper, we deal with the existence of at least one and of at least two positive solutions as well the uniqueness of a positive solution for an...

Existence and uniqueness of positive solution for nonlinear difference equations involving p(k)-Laplacian operator

Published Online: Mar 02, 2019

Page range: 141 - 167

Received: Jan 30, 2018

Accepted: Jun 12, 2018

DOI: https://doi.org/10.2478/auom-2019-0008

Keywords
Discrete nonlinear boundary value problem, Non trivial solution, Variational methods, Critical point theory

© 2019 Mohsen Khaleghi Moghadam et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Existence and uniqueness of positive solution for nonlinear difference equations involving p(k)-Laplacian operator

Published Online: Mar 02, 2019

Page range: 141 - 167

Received: Jan 30, 2018

Accepted: Jun 12, 2018

DOI: https://doi.org/10.2478/auom-2019-0008

KeywordsDiscrete nonlinear boundary value problem, Non trivial solution, Variational methods, Critical point theory

© 2019 Mohsen Khaleghi Moghadam et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Discrete nonlinear boundary value problem, Non trivial solution, Variational methods, Critical point theory