Existence And Multiplicity Of Solutions For A Class Of Second-order Difference Equation Neumann Boundary Value Problems

Based on the improtant research background and status analysis of the differ-ence equation Neumann boundary value problem,this paper mainly discussed the existence and multiplicity of(positive)solutions of the following three kinds of value problems:Firstly,by using fixed point index theory in cones,we obtain the existence and multiplicity of positive solutions semipositone second-order difference equation Neu-mann boundary value problem with variable coefficient where f:[1,T]Z×[0,+?)?[-M,+?)is continuous,[1,T]Z:={1,2,…,T},M>0 is constant.Secondly,by using the method of the upper and lower solutions and topological degree theory,we obtain the relationship between s and the number of solutions for the second-order difference equation Neumann boundary value problem where s?R is real parameter,g:[1,T]Z×R?R is continuous.Lastly,by using the Leray-Schauder theory,we study the existence of solutions for second-order Neumann boundary value problem at resonance where e:[1,T]Z?R,f:[1,T]Z×R2?R is continuous and satisfies barrier strips conditions.