| Summary: | 碩士 === 靜宜大學 === 應用數學研究所 === 94 === Consider the eigenvalue of the Laplace operator on the surfaces of revolution S：
Δu+λu=0 u=0 on boundary S.
Using separation of variable, we can transform a Laplace operator into a Sturm-Liouville operator. Through the study on the Sturm-Liouville eigenvalue problem, we obtain the variation of the first eigenvalues of the Laplace operator.According to the location of the band region with fixed area on S.
Indeed, we obtain the following results：When the generating function is f(x)=ax+b>0 .IF a>0, the first eigenvalue is increasing as the band region moves to the right side. Otherwise, the first eigenvalue is decreasing. When the generating function is f(x)=x^3>0 . The first eigenvalue is increasing as the band region moves to the right side.
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