CAJ | 학술논문

含一个参数的一阶微分方程边值问题是指：含有未知量及它的一阶导数的方程的定解条件不仅依赖于在区间端点的取值,而且依赖于方程中的参数.通常它用不动点定理或逐步逼近法来解决.文章利用上下解方法和单调迭代技术讨论了含有一个参数的微分问题极值解的存在性,通过构造单调序列使这个单调序列一致收敛于非线性方程的极值解.
함일개삼수적일계미분방정변치문제시지：함유미지량급타적일계도수적방정적정해조건불부의뢰우재구간단점적취치,이차의뢰우방정중적삼수.통상타용불동점정리혹축보핍근법래해결.문장이용상하해방법화단조질대기술토론료함유일개삼수적미분문제겁치해적존재성,통과구조단조서렬사저개단조서렬일치수렴우비선성방정적겁치해.
The boundary value problem for first-order differential equations with a parameter refers to the finite solution condition of equation which includes unknown quantity and its first-order derivative that not only relies on interval value but also relies on the parameter of the equation, which is always settled by fixed point theory or successive approximation meth- od. This paper considers existence of extreme solutions to first-order differential equations with a parameter by the method of lower and upper solutions with monotone iterations,and monotonic sequence is uniformly converged to the extreme value solution of nonlinear equation after being constructed.