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Search: MSC category 35B05 ( Oscillation, zeros of solutions, mean value theorems, etc. )

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1. CMB 2009 (vol 53 pp. 153)

Niu, Pengcheng; Ou, Yafei; Han, Junqiang
Several Hardy Type Inequalities with Weights Related to Generalized Greiner Operator
In this paper, we establish several weighted $L^p (1\lt p \lt \infty)$ Hardy type inequalities related to the generalized Greiner operator by improving the method of Kombe. Then the best constants in inequalities are discussed by introducing new polar coordinates.

Keywords:generalized Greiner operator, polar coordinates, Hardy inequality
Categories:35B05, 35H99

2. CMB 2005 (vol 48 pp. 405)

Froese, Richard
Liouville's Theorem in the Radially Symmetric Case
We present a very short proof of Liouville's theorem for solutions to a non-uniformly elliptic radially symmetric equation. The proof uses the Ricatti equation satisfied by the Dirichlet to Neumann map.

Categories:35B05, 34A30

3. CMB 1997 (vol 40 pp. 244)

Naito, Yūki; Usami, Hiroyuki
Nonexistence results of positive entire solutions for quasilinear elliptic inequalities
This paper treats the quasilinear elliptic inequality $$ \div (|Du|^{m-2}Du) \geq p(x)u^{\sigma}, \quad x \in \Rs^N, $$ where $N \geq 2$, $m > 1$, $ \sigma > m - 1$, and $p \colon \Rs^N \rightarrow (0, \infty)$ is continuous. Sufficient conditions are given for this inequality to have no positive entire solutions. When $p$ has radial symmetry, the existence of positive entire solutions can be characterized by our results and some known results.

Categories:35J70, 35B05

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