讨论非局部边界条件下一类具有非退化拟线性抛物型偏微分方程解的性质，通过运用上、下解和单调迭代的方法,得到抛物型问题解的存在唯一性以及椭圆问题最大、最小解的存在性.同时，还得到发展方程解对平衡解的渐近性态.

This paper concerns a class of quasi-linear parabolic and elliptic partial differential equations in a bounded domain with nonlocal boundary conditions. The equations under consideration are non-degenerate depending on the property of the diffusion coefficient. By using the upper and lower solutions and monotone iteration, the aim of the paper is to show existence and uniqueness of solutions for the time-dependent problem, existence of maximal and minimal steady-state solutions of the elliptic problem, and the asymptotic behavior of the time-dependent solutions in relation to the steady-state solutions.