Solutions of the boundary value problem for a 2nth-order nonlinear difference equation containing both advance and retardation

Existence of Nontrivial Solutions of a Two Point Boundary Value Problem for a 2nth Order Nonlinear Difference Equation

We will show how to use the mountain pass theorem to obtain nontrivial solutions of a certain two point BVP for the 2nth order, n ∈ N (formally) self-adjoint nonlinear difference equation n ∑ i=0 [ri(t) u(t − i)] = f (t, u(t)), t ∈ [a, b]Z. No periodicity assumptions will be placed on ri, i = 0, 1, . . . , n or f and it will be assumed that f grows superlinearly both at the origin and at infini...

Solutions of 2nth-Order Boundary Value Problem for Difference Equation via Variational Method

The variational method and critical point theory are employed to investigate the existence of solutions for 2nth-order difference equation Δ pk−nΔyk−n −1 n f k, yk 0 for k ∈ 1,N with boundary value condition y1−n y2−n · · · y0 0, yN 1 · · · yN n 0 by constructing a functional, which transforms the existence of solutions of the boundary value problem BVP to the existence of critical points for t...

Existence of positive solutions for a boundary value problem of a nonlinear fractional differential equation

This paper presents conditions for the existence and multiplicity of positive solutions for a boundary value problem of a nonlinear fractional differential equation. We show that it has at least one or two positive solutions. The main tool is Krasnosel'skii fixed point theorem on cone and fixed point index theory.

Triple Positive Solutions for Boundary Value Problem of a Nonlinear Fractional Differential Equation

existence of positive solutions for a boundary value problem of a nonlinear fractional differential equation

this paper presents conditions for the existence and multiplicity of positive solutions for a boundary value problem of a nonlinear fractional differential equation. we show that it has at least one or two positive solutions. the main tool is krasnosel'skii fixed point theorem on cone and fixed point index theory.