Ground State Solutions of Discrete Asymptotically Linear Schrödinger Equations with Bounded and Non-periodic Potentials

Homoclinic Solutions for a Higher Order ϕc‐Laplacian Difference Equation Containing Both Advance and Retardation

“…On the other hand, we notice that the nonlinear term f is only either superlinear or asymptotically linear at ∞ which plays an important role in the existence of homoclinic solutions when the similar arguments were considered in many references [25][26][27][28]. But in this paper, the nonlinearities can be mixed superlinear with asymptotically linear at ∞, see Remark 1 for details.…”

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].…”