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Existence of entire explosive positive radial solutions of sublinear elliptic systems. (English) Zbl 1005.35038
Summary: Our main purpose is to establish the existence of entire explosive positive radial solutions of the quasilinear elliptic system $$\text{div} \bigl(|\nabla u|^{p-2}\nabla u\bigr)= m \bigl(|x|\bigr)v^\alpha,\ x\in\Bbb R^N$$ $$\text{div}\bigl( |\nabla v|^{q-2}\nabla v\bigr)= n\bigl(|x|\bigr) u^\beta,\ x\in \Bbb R^N$$ where $0<\alpha\le p-1$, $0<\beta\le q-1$. The main results of the present paper are new and extend the previously known results [see, for example, {\it A. V. Lair} and {\it A. W. Wood}, J. Differ. Equations 164, No. 2, 380--394 (2000; Zbl 0962.35052)].

35J45Systems of elliptic equations, general (MSC2000)
35A05General existence and uniqueness theorems (PDE) (MSC2000)
Full Text: DOI
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