Positive solutions of a singular positone and semipositone boundary value problems for fourth-order difference equations (Q607901)

Summary: The author studies the boundary value problems for the fourth-order nonlinear singular difference equations \[ \Delta ^{4}u(i - 2)=\lambda\alpha(i)f(i,u(i)),\quad i\in [2,T+2],\;u(0)=u(1)=0,\;u(T+3)=u(T+4)=0. \] He shows the existence of positive solutions for positone and semipositone 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.