×

zbMATH — the first resource for mathematics

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
PDF BibTeX XML Cite
Full Text: DOI