Power functions with low uniformity on odd characteristic finite fields
In this paper, we give some new low differential uniformity of some power functions defined on finite fields with odd characteristic. As corollaries of the uniformity, we obtain two families of almost perfect nonlinear functions in GF(3 n ) and GF(5 n ) separately. Our results can be used to prove the Dobbertin et al.’s conjecture.
In this work, we study the existence and multiplicity of positive solutions for the higher order p-Laplacian boundary value problem with even derivatives