Abstract
Abstract We prove the existence of weak solutions for an anisotropic homoclinic discrete nonlinear system. Suitable Hilbert spaces and norms are constructed. The proof of the main result is based on a minimization method. We also extend the problem by using generalized penality and source functions.
Highlights
In this paper, we investigate the existence of weak solutions for the following anisotropic nonlinear discrete system.For i =, · · ·, n −∆ α(k − )a(k −, ∆ui(k − ))+ |ui(k)|p(k)− ui(k) = fi(k, u(k)), k ∈ Z (1.1) lim |k|→+∞ ui(k) =
We prove the existence of weak solutions for an anisotropic homoclinic discrete nonlinear system
We investigate the existence of weak solutions for the following anisotropic nonlinear discrete system
Summary
We investigate the existence of weak solutions for the following anisotropic nonlinear discrete system. The di erence equations is the discrete counterpart of PDEs and are usually studied in connection with numerical analysis. In this way, the main operator in problem (1.1). We adapt the classical minimization methods used for the study of anisotropic PDEs to prove the existence of solution of problem (1.1). We consider a system of n equations where the source function f depends on the solution u(.) = u (.), · · · , un(.) ∈ Rn. we make an extension of the main problem where we observe a competition phenomena between the functions α and σ.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
