In this paper, some new classes of permutation polynomials with the form 071579716300041&_mathId=si1.gif&_user=111111111&_pii=S1071579716300041&_rdoc=1&_issn=10715797&md5=6dbbbefdd47b8bd63fecab59cf3c1eaf" title="Click to view the MathML source">(xpm−x+δ)s+x are investigated by determining the number of solutions of some equations over 071579716300041&_mathId=si2.gif&_user=111111111&_pii=S1071579716300041&_rdoc=1&_issn=10715797&md5=7a14e396b04cf19a938d8c5bac11e92a" title="Click to view the MathML source">Fp2m.