一类非线性椭圆型方程非局部ROBIN边值问题(英文)

A Class of Nonlocal Robin Boundary Value Problems of Nonlinear Elliptic Equation

研究了一类非线性非局部椭圆型方程奇摄动Robin边值问题.在适当的条件下,首先建立了相应问题的比较定理.其次求出了原问题的外部解.然后利用伸长变量、合成展开法和幂级数展开理论构造出解的边界层项,并由此得到解的形式渐近展开式.最后利用微分不等式理论,讨论了问题解的渐近性态,讨论了原问题解的存在性和解的一致有效的渐近估计式.

A class of nonlinear nonlocal singularly perturbed Robin boundary value problems for elliptic equation is considered.Under suitable conditions,firstly,the comparison theorem for the corresponding problem is constituted.Secondly,the outer solution of the original problem is obtained.And then,using the stretched variable,the composing expansion method and the expanding theory of power series the boundary layer is constructed.Finally,using the theory of differential inequalities the asymptotic behavior of solution for the boundary value problems is studied and the uniformly valid asymptotic estimation is discussed.