Existence theorems for second-order discrete boundary value problems☆

By Xiaochun Cai, Jianshe Yu. 2006

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Multiple homoclinic solutions for the discrete p-Laplacian via critical point theory (2013, methodology): “employed by Agarwal, Perera and O’Regan [3] and then successfully applied by several authors: wemention here the works of Cabada, Iannizzotto and Tersian [7], Cai and Yu [9], Candito and Giovannelli [10], Faraci and Iannizzotto [14], Jiang and Zhou [15], Mihăilescu, Rădulescu and Tersian [20] (for t”
Multiple solutions for discrete boundary value problems (2009, methodology): “Key words and phrases: Difference equations, Discrete p–Laplacian, Variational methods.”
Eigenvalue problems for anisotropic discrete boundary value problems (2009, background): “It can be verified (see [4]) that T (2−m)/(2m) · |u|2 ≤ |u|m ≤ T 1/m · |u|2, ∀ u ∈ H and m ≥ 2 .”
Existence of Periodic and Subharmonic Solutions for Second-Order p-Laplacian Difference Equations (2007, background): “1) depends on xn+1 and xn−1, the traditional ways of establishing the functional in [2–7] are inapplicable to our case.”