On the zeros of solutions of elliptic equations with deviating arguments (Q1336219)

The existence of zeros of solutions of parabolic or hyperbolic partial differential equations of neutral type has been intensively studied during the last decades. By contrast, there are only few results for elliptic equations with deviating arguments. One of them is Tramov's result on homogeneous elliptic equations with deviating arguments [\textit{M. I. Tramov}, Differ. Uravn. 20, No. 4, 721-723 (1984; Zbl 0598.35123)]. Generalizing Tramov's approach the author investigates the elliptic equation with forcing term \[ \Delta u(x - \sigma) + p(x) u(x - \tau) = f(x), \tag{1} \] and presents some conditions which imply that every solution of (1) has a zero in bounded domains of \(\mathbb{R}^n\).