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Distribution of eigenvalues of a two-parameter system of differential equations

Distribution of eigenvalues of a two-parameter system of differential equations

In this paper two simultaneous Sturm-Liouville systems are considered, the first defined for the interval <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="0 less-than-or-slanted-equals x 1 less-than-or-slanted-equals 1"> <mml:semantics> <mml:mrow> <mml:mn>0</mml:mn> <mml:mspace width="thinmathspace" /> <mml:mo>⩽<!-- ⩽ --></mml:mo> <mml:mspace width="thinmathspace" /> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>x</mml:mi> <mml:mn>1</mml:mn> </mml:msub> </mml:mrow> <mml:mspace width="thinmathspace" /> <mml:mo>⩽<!-- ⩽ --></mml:mo> …