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Oscillation theorems for second-order half-linear differential equations. (English) Zbl 0877.34027

From the authors’ summary: Oscillation criteria for the second-order half-linear differential equation \[ [r(t)|x'(t)|^{\alpha-1}x'(t)]'+ p(t)|x(t)|^{\alpha-1}x(t)=0,\quad t\geq t_0 \] are established, where \(\alpha>0\) is a constant and \(\int^\infty_t p(s)ds\) exists for \(t\in[t_0,\infty)\). We apply these results to the following equation: \[ \sum^N_{i=1} D_i(|Du(x)|^{n-2}D_iu(x))+ c(|x|)|u(x)|^{n-2}u(x)=0,\quad x\in\Omega_a, \] where \(D_i={\partial\over\partial x_i}\), \(D=(D_1,\dots,D_N)\), \(\Omega_a= \{x\in\mathbb{R}^N:|x|\geq a\}\) is an exterior domain, and \(c\in C([a,\infty),\mathbb{R})\), \(n>1\) and \(N\geq 2\) are integers. Here, \(a>0\) is a given constant.
Reviewer: P.Smith (Keele)

MSC:

34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
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