具有不连续系数的三阶半线性奇异摄动边值问题

Singularly perturbed third-order semilinear boundary value problems with discontinuous coefficients

主要研究了一类具有不连续系数的奇异摄动边值问题解的存在性和渐近估计.首先,利用Schauder不动点定理,建立一般问题的上下解定理;其次,利用边界函数法,构造出形式渐近解,并基于已确立的上下解定理,证明解的存在性和一致有效性;最后给出实例验证主要结论.

The existence and asymptotic estimates of solutions for a class of singularly perturbed boundary value problems with discontinuous coefficients are investigated in this paper. Firstly, by using the Schauder fixed point theorem, a theorem of lower-upper solutions for general problems is established. Secondly, the formal asymptotic solution is constructed by the method of boundary functions, and the existence and uniform validity of the solution are proved by using the theorem of lower-upper solutions. Finally, an example is presented as an illustration.