Some new oscillation criteria for second order elliptic equations with damping
Volume 86 / 2005
Annales Polonici Mathematici 86 (2005), 31-42
MSC: 35B05, 34C10.
DOI: 10.4064/ap86-1-4
Abstract
Some new oscillation criteria are obtained for second order elliptic differential equations with damping $$\sum_{i,j=1}^nD_i[A_{ij}(x)D_jy]+\sum_{i=1}^nb_i(x)D_iy+q(x)f(y)=0,\ \quad x\in{\mit\Omega},$$ where ${\mit\Omega} $ is an exterior domain in $\mathbb R^n$. These criteria are different from most known ones in the sense that they are based on the information only on a sequence of subdomains of ${\mit\Omega}\subset \mathbb R^n$, rather than on the whole exterior domain ${\mit\Omega}$. Our results are more natural in view of the Sturm Separation Theorem.
