He introduced one of the approaches to the inverse scattering problem for Sturm–Liouville operators, and derived what is now called the Marchenko equation.
Schrödinger equation | Nernst equation | Monge–Ampère equation | Boltzmann equation | Diophantine equation | Anatoly Marchenko | Ordinary differential equation | ordinary differential equation | Young–Laplace equation | Wave equation | wave equation | Vlasov equation | Vladimir Marchenko | Tait equation | Smoluchowski coagulation equation | Sauerbrey equation | Redlich–Kwong equation of state | Ramanujan–Nagell equation | Quadratic equation | Prony equation | Pell's equation | Mathieu's equation | Marchenko equation | Majorana's equation | Linear equation | linear equation | Liénard equation | Kepler's equation | Kaup–Kupershmidt equation | Ishimori equation |