This chapter combines the findings of the previous two. The solution criterion for indefinite Sturm–Liouville problems is applied to a sequence of these problems that were shown to be, as a whole, unitarily equivalent to the original problem of divergence form with sign-changing coefficients. The eventual solution criterion can be reduced to finding roots of polynomials with coefficients being rational functions in the coefficients of the original problem.

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The Higher-dimensional Problem: Well-posedness

  • Marcus Waurick

摘要

This chapter combines the findings of the previous two. The solution criterion for indefinite Sturm–Liouville problems is applied to a sequence of these problems that were shown to be, as a whole, unitarily equivalent to the original problem of divergence form with sign-changing coefficients. The eventual solution criterion can be reduced to finding roots of polynomials with coefficients being rational functions in the coefficients of the original problem.