CAJ | 학술논문

研究了一类具有转换条件且两个边界条件中带谱参数的正则Sturm-Liouville问题.应用常数变易法导出Sturm-Liouville初值问题的一对线性无关的基本解的表达式,然后将该问题的基本解的渐近分析,转化为考虑定义在适当的Hilbert空间H中的一个线性自伴算子A的基本解的渐近分析,并推导出该正则的Sturm-Liouville算子A的基本解的渐近式和整函数的渐近式.
연구료일류구유전환조건차량개변계조건중대보삼수적정칙Sturm-Liouville문제.응용상수변역법도출Sturm-Liouville초치문제적일대선성무관적기본해적표체식,연후장해문제적기본해적점근분석,전화위고필정의재괄당적Hilbert공간H중적일개선성자반산자A적기본해적점근분석,병추도출해정칙적Sturm-Liouville산자A적기본해적점근식화정함수적점근식.
To investigate a class of regular Sturm-Liouville problems with transmission conditions and spectral-parameter in two boundary conditions,we applied the constants method to derive the expressions of a pair of linear independent fundamental solutions of Sturm-Liouville initial-value problems.Then a self-adjoint linear operator A ws defined in a suitable Hilbert space H such that the analysis of such problem were transformed into those of operator A.The asymptotic formulas of fundamental solutions of the regular Sturm-Liouville operator and integral function were also given.