Liquid-state integral equations at high density: On the mathematical origin of infinite-range oscillatory solutions

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Abstract
Analytic asymptotic analysis and finite element numerical procedures are used to elucidate the mathematical reasons for the appearance of infinite‐range oscillatory solutions to certain integral equation theories of wall–fluid interfacial structure and liquid state radial distribution functions. The results contribute to two issues of recent debate: (i) what physical significance (if any) can be attributed to the apparent ‘‘solidlike’’ structure that is often (but not always) seen in high density solutions to liquid state integral equation theories and (ii) is the same mathematical structure present in density functional theories (i.e., in the presence of a variational condition arising from a free energy functional)?