On nonnegative radial entire solutions of second order quasilinear elliptic systems

T. Teramoto, Hiroshima University, Higasi-Hiroshima, Japan

E. J. Qualitative Theory of Diff. Equ., No. 16. (2002), pp. 1-34.

Abstract: In this article we consider the second order quasilinear elliptic system of the form
$$\Delta_{p_i} u_i=H_i(|x|)u_{i+1}^{\alpha_i}, x\in R^N, i=1,2,...,m$$
with nonnegative continuous function $H_i$. Sufficient conditions are given to have nonnegative nontrivial radial entire solutions. When $H_i$, $i = 1, 2, ..., m$, behave like constant multiples of $|x|^\lambda$, $\lambda\in R$, we can completely characterize the existence property of nonnegative nontrivial radial entire solutions.

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