Some new oscillation criteria for second order elliptic equations with damping

Rong-Kun Zhuang¹ ; Zheng-an Yao²

¹ Department of Mathematics Huizhou University Huizhou, Guangdong 516015, P.R. China
² Department of Mathematics Sun Yat-Sen (Zhongshan) University Guangzhou 510275, P.R. China

Annales Polonici Mathematici, Tome 86 (2005) no. 1, pp. 31-42.

Résumé

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.

Détail

DOI : 10.4064/ap86-1-4

Keywords: oscillation criteria obtained second order elliptic differential equations damping sum sum y quad mit omega where mit omega exterior domain mathbb these criteria different known sense based information only sequence subdomains mit omega subset mathbb rather whole exterior domain mit omega results natural view sturm separation theorem