The Study Of Existence Of Positive Solutions For Some Second-Order Nonlinear Difference Equations

In this paper we study the existence of positive solutions for some second-order nonlinear difference equations. For different difference equations, we first assume that the nonlinearities have the properties of semipositone and monotonicity. Then we prove the existence of positive solutions for difference equations by using fixed point theorem of cone expansion and compression. In addition, when the nonlinearities have the properties of mixed-monotonicity, the existence of a positive solution for difference equations is ob-tainded by using fixed point theorem in a cone or fixed point theorem of conic expansion and compression. Finally, some nonlinear eigenvalue problems are discussed. We get the existence of positive solutions for difference equations by using appoximation and fixed point theorem of conic expansion and compression.