Electron. J. Diff. Equ., Vol. 2011 (2011), No. 151, pp. 1-11.

Oscillation criteria for damped quasilinear second-order elliptic equations

Tadie

Abstract:
In 2010, Yoshida [13] stated that oscillation criteria for the superlinear-sublinear elliptic equation equation
$$ \nabla \cdot \big(A(x)\Phi(\nabla v)\big) + (\alpha+1)B(x)\cdot\Phi(\nabla v) + C(x) \phi_\beta(v) + D(x) \phi_\gamma (v)=f(x) $$
were not known. In this article, we provide some answers to this question using boundedness conditions on the coefficients of half-linear quasilinear elliptic equations. This is obtained by using some comparison methods and Picone-type formulas.

Submitted July 21, 2011. Published November 8, 2011.
Math Subject Classifications: 34C10, 34K15, 35J70.
Key Words: Picone; oscillation criteria for half-linear elliptic equations.

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Tadie
Mathematics Institut
Universitetsparken 5
2100 Copenhagen, Denmark
email: tadietadie@yahoo.com, tad@math.ku.dk

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