Nonexistence results of positive entire solutions for quasilinear elliptic inequalities. (English) Zbl 0879.35062
Summary: This paper treats the quasilinear elliptic inequality
\[
\text{div}(|Du|^{m-2}Du)\geq p(x)u^\sigma,\quad x\in\mathbb{R}^N,
\]
where \(N\geq 2\), \(m>1\), \(\sigma>m-1\), and \(p:\mathbb{R}^N\to(0,\infty)\) 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.
MSC:
35J85 | Unilateral problems; variational inequalities (elliptic type) (MSC2000) |
35J60 | Nonlinear elliptic equations |
35B05 | Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs |