On the Zeros of Some Well-Known Equations

The number of zeros of solutions of some rather general equations are studied. The considered equations imply as particular cases time independent versions of some partial differential equations (among them Schrödinger’s, Fisher’s, Zeldovich’s, Korteweg–de Vries’ equations), as well as imply some ordinary differential equations (among them Emden-Fowler’s, Sturm–Liouville’s, Van der Pol’s equations). As far as we know the number of zeros was studied only for Sturm–Liouville type equations (including the Schrödinger equations) and for other listed above equations the results are brand new.