By using fixed-point theorem in cones and fixed-point index theory,a class of discrete P-Laplacian boundary value problem was discussed and a sufficient condition of existence of one or two positive solutions was obtained.

This paper presents an algorithm based on fixed-point theorem and Quine.

By means of Darbo s fixed-point theorem,an existence result of solution for two-point boundary value problem of nonlinear fractional differential equation is obtained.

Common fixed point theorems for Altman type mappings;

With the help of Maximum principle,Picard existence and uniqueness theorem and LeraySchauder fixed point theorems,the existence and uniqueness of the solution of nonlinear coupled differentio-integral system whose geometrical model is area-preserving curvature flow on the plane are proved.

Using the fixed point theorems of cone mapping,a method is given to decide the existence of positive solution of second order two points boundary value problem with sign change of nonlinearities.