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Positive solutions of a singular positone and semipositone boundary value problems for fourth-order difference equations. (English) Zbl 1204.39012

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.

MSC:

39A22 Growth, boundedness, comparison of solutions to difference equations
39A10 Additive difference equations
39A12 Discrete version of topics in analysis
34B16 Singular nonlinear boundary value problems for ordinary differential equations
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