一类非线性高阶q-对称差分方程解的存在性

Existence of solutions for a class of nonlinear high order q-symmetric difference equations

研究一类非线性高阶q-对称差分方程解的存在性,通过计算得出解的表达形式,利用Banach空间完全连续算子的不动点定理得出解的存在唯一性结果,应用Schaefer's不动点定理得出解的存在性。

We consider the existence of solutions for a class of nonlinear high order q-symmetric difference equations.The solution of BVP is acquired by calculating.We construct a Banach space and get the uniqueness of solution by making use of Banach space completely continuous operator's fixed theorem,and the existence of the solutions is obtained by using the Schaefer's fixed point theorem.The proofs of these results is based on Banach space completely continuous operator's fixed theorem and Schaefer's fixed point theorem.