Geodesic
Annulus oscillation criteria for second order nonlinear elliptic differential equations with damping
Electronic Journal of Differential Equations, Tome 2009 (2009).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We establish oscillation criteria for the second-order elliptic differential equation $$ \nabla\cdot(A(x)\nabla y)+B^T(x)\nabla y+q(x)f(y)=e(x), \quad x\in\Omega, $$ 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.
Classification : 35J60, 34C10
Keywords: nonlinear elliptic differential equation, second order, oscillation, annulus criteria 
@article{EJDE_2009__2009__a105,
     author = {Zhuang, Rong-Kun},
     title = {Annulus oscillation criteria for second order nonlinear elliptic differential equations with damping},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2009},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2009__2009__a105/}
}
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Zhuang, Rong-Kun. Annulus oscillation criteria for second order nonlinear elliptic differential equations with damping. Electronic Journal of Differential Equations, Tome 2009 (2009). http://geodesic.mathdoc.fr/item/EJDE_2009__2009__a105/