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Large Solutions to Elliptic Systems of $$\infty$$-Laplacian Equations
- Source :
- Mathematical Notes. 109:971-979
- Publication Year :
- 2021
- Publisher :
- Pleiades Publishing Ltd, 2021.
-
Abstract
- In this paper, we study the existence, uniqueness and boundary behavior of positive boundary blow-up solutions to the quasilinear system $$\Delta_{\infty}u=a(x)u^{p}v^{q}$$ , $$\Delta_{\infty}v=b(x)u^{r}v^{s}$$ in a smooth bounded domain $$\Omega\subset R^{N}$$ , with the explosive boundary condition $$u=v=+\infty$$ on $$\partial\Omega$$ , where the operator $$\Delta_{\infty}$$ is the $$\infty$$ -Laplacian, the positive weight functions $$a(x)$$ , $$b(x)$$ are Holder continuous in $$\Omega$$ , and the exponents verify $$p$$ , $$s > 3$$ , $$q$$ , $$r>0$$ , and $$(p-3)(s-3) > qr$$ .
Details
- ISSN :
- 15738876 and 00014346
- Volume :
- 109
- Database :
- OpenAIRE
- Journal :
- Mathematical Notes
- Accession number :
- edsair.doi...........47ec67f9c9721112ec8195a5a7ad5855