Positive solutions of boundary value problem for singular positone and semi-positone third-order difference equations

Abstract

Abstract This article studies the boundary value problems for the third-order nonlinear singular difference equations Δ 3 u ( i - 2 ) + λ a ( i ) f ( i , u ( i ) ) = 0 , i ∈ [ 2 , T + 2 ] , satisfying five kinds of different boundary value conditions. This article shows the existence of positive solutions for positone and semi-positone type. The nonlinear term may be singular. Two examples are also given to illustrate the main results. The arguments are based upon fixed point theorems in a cone. MSC [2008]: 34B15; 39A10.

Keywords

• positive solution
• positone and semi-positone boundary value problem
• singular difference equation
• fixed point theorem