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The existence of large solutions of non-variational type singular quasilinear elliptic system on $${{\text{R}}^N}$$. (Chinese. English summary) Zbl 1413.35219
Summary: This paper considers a class of non-variational type singular quasilinear elliptic system: ${\text{div}}\left ( {{{\left| x \right|}^{ - ap}}{{\left| {\nabla u} \right|}^{p - 2}}\nabla u} \right) = f\left ( x \right){u^\alpha}{v^\gamma},\;{\text{div}}\left ( {{{\left| x \right|}^{-bq}}{{\left| {\nabla v} \right|}^{q-2}}\nabla v} \right) = g\left ( x \right){u^\delta}{v^\beta}, x \in {{\text{R}}^N},$ with $$u\left ( x \right)$$, $$v\left ( x \right) > 0$$, and $$u\left ( x \right)$$, $$v\left ( x \right) \to + \infty$$ as $$\left| x \right| \to + \infty$$, where $$0 \leq \alpha < p - 1$$, $$0 \leq \beta < q - 1$$, $$\gamma, \delta > 0$$, $$0 \leq a < \left ( {N - p} \right)/p$$, $$0 \leq b < \left ( {N - q} \right)/q$$, and $$\sigma = \left ( {p - 1 - \alpha} \right)\left ( {q - 1 - \beta} \right) - \gamma \delta < 0$$. Through constructing the upper and lower solution method, it is proved that, under appropriate conditions, there is at least one set of large solutions to this equation system.
##### MSC:
 35J62 Quasilinear elliptic equations 35J75 Singular elliptic equations
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