Abstract
In this paper, we consider the existence of homoclinic solutions for a class of nonlinear difference systems involving classical $(\phi_{1}, \phi_{2})$ -Laplacian. First, we improve some inequalities in known literature. Then, by using the variational method, some new existence results are obtained. Finally, some examples are given to verify our results.
Highlights
Introduction and main results LetR denote the real numbers and Z the integers
We investigate the existence of homoclinic solutions for the following nonlinear difference systems involving classical (φ, φ )-Laplacian: φ ( u (t – )) + ∇u V (t, u (t), u (t)) = f (t), ( . )
Φ ( u (t – )) + ∇u V (t, u (t), u (t)) = f (t), where t ∈ Z, um(t) ∈ RN, m =, V (t, x, x ) = –K (t, x, x ) + W (t, x, x ), K, W : Z × RN × RN → R and φm, m =, satisfy the following condition: (A ) φm is a homeomorphism from RN onto RN such that φm( ) =, φm = ∇ m, with m ∈ C (RN, [, +∞]) strictly convex and m( ) =, m =
Summary
Introduction and main results LetR denote the real numbers and Z the integers. Given a < b in Z. Assume that (A ) holds, fi = , i = , , W and K satisfy the following conditions: (V) V (t, x , x ) = –K (t, x , x ) + W (t, x , x ), where K , W : Z × RN × RN → R, K (t, x , x )
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.
