Annulus oscillation criteria for second order nonlinear elliptic differential equations with damping

Abstract

We establish oscillation criteria for the second-order elliptic differential equation $$ ablacdot(A(x) abla y)+B^T(x) abla y+q(x)f(y)=e(x), quad xinOmega, $$ where $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 annulus of $Omega$, rather than on the whole exterior domain $Omega$. Both the cases when $frac{partial b_i}{partial x_i}$ exists for all $i$ and when it does not exist for some $i$ are considered.

Keywords

• Nonlinear elliptic differential equation
• second order
• oscillation
• annulus criteria