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

We consider a 2mth-order nonlinear difference equation containing both advance and retardation with ϕc-Laplacian. Using the critical point theory, some new and concrete criteria for the existence of homoclinic solutions with mixed nonlinearities are obtained.

Fractional Differential Equation Involving Mixed Nonlinearities with Nonlocal Multi-Point and Riemann-Stieltjes Integral-Multi-Strip Conditions

In this paper, we investigate a new class of boundary value problems involving fractionaldifferential equations with mixed nonlinearities, and nonlocal multi-point and Riemann–Stieltjesintegral-multi-strip boundary conditions. Based on the standard tools of the fixed point theory,we obtain some existence and uniqueness results for the problem at hand, which are well illustratedwith the aid of examples. Our results are not only in the given configuration but also yield severalnew results as special cases. Some variants of the given problem are also discussed.