Homoclinic Solutions of Discrete Nonlinear Systems via Variational Method

Large Constant-Sign Solutions of Discrete Dirichlet Boundary Value Problems with p-Mean Curvature Operator

“…Many authors have discussed the existence and multiplicity of solutions for difference equations through classical tools of nonlinear analysis: Fixed point theorems, upper and lower solutions techniques; see [7,9] and the references given therein. Since 2003, by starting from the seminal paper [18], variational methods have been used to investigate nonlinear difference equations, which have obtained various results; see [19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34].…”

Positive Solutions for a Class of Discrete Mixed Boundary Value Problems with thep,q-Laplacian Operator

“…In recent years, with the development of mechanical engineering, control system, computer science, and economics, the existence of solutions of difference equations has attracted wide attention (see [1][2][3][4][5][6]). For example, applying Ricceri variational principle to obtain the existence of multiple solutions [7][8][9], taking the invariant sets of descending flow to prove the existence of sign-changing solutions [10], making the linking theorem to get the existence and multiplicity of periodic solutions [11], and using critical point theory to obtain the existence of homoclinic solutions [12][13][14][15] and heteroclinic solutions [16].…”

Infinitely Many Positive Solutions for a Coupled Discrete Boundary Value Problem

“…In recent years, variational methods have been employed to study difference equation and various results have been obtained. See, for instance, [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22].…”