具有不连续系数的奇异摄动拟线性边值问题（英文）

Singularly perturbed quasilinear boundary value problems with discontinuous coefficients

研究一类具有不连续系数的奇异摄动二阶拟线性边值问题,其解因一阶导数的不连续性而出现内部层.用合成展开法和上下解定理得到所提问题内部层解的存在性和渐近估计.所得结果应用到由Farrell等(Farrell P A,O'Riordan E,Shishkin G.A class of singularly perturbed quasilinear differential equations with interiors layers.Mathematics ofComputation,2009,78:103-127)所提出的一个特殊拟线性问题.

A class of singularly perturbed boundary value problems of second order quasilinear differential equations with discontinuous coefficients, whose solu- tions exhibit an interior layer caused by the discontinuity of the coefficient of the first order derivative, are investigated in this paper. By the composite expansion method and the theorem of lower and upper solutions, the existence and asymptotic estimates of solution with the interior layer for the proposed problem are obtained. The result is applied to a special quasilinear problem proposed by Farrell, et al. （Farrell P A, O＇Riordan E, Shishkin G. A class of singularly perturbed quasilinear differential equations with interiors layers. Mathematics of Computation, 2009, 78： 103-127）.