Entire large positive radial symmetry solutions for combined quasilinear elliptic system

Authors: SESHADEV PADHI, SMITA PATI

Abstract: We prove the existence of entire large positive solutions to the system \begin{equation*} \begin{cases} (r^{N-1}\phi_{1}(u^{\prime}))^{\prime} = r^{N-1}P_{1}(r)f(u,v),\, \, 0 \leq r < \infty \\ (r^{N-1}\phi_{2}(v^{\prime}))^{\prime} = r^{N-1}P_{2}(r)g(u,v),\, \, 0 \leq r < \infty \\ u(0) = a, \, v(0) = b, \, u^{\prime}(0) = 0, \, v^{\prime}(0) = b, \end{cases} \end{equation*} where the functions $\phi_{i}(s) = \alpha_{i}(s^{2})s, \,\, i= 1, 2$ are odd, increasing homeomorphisms, $P_{1},P_{2}:[0,\infty)\to [0,\infty)$ are continuous, and $f,g:[0,\infty) \times [0,\infty) \to [0,\infty)$ are continuous and increasing functions.

Keywords: Elliptic system, positive solutions, radial solutions, large solutions

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