Asymptotic behavior of solutions of nonlinear elliptic equations
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We study and obtain formulas for the asymptotic behavior as |x|→∞ of C2 solutions of the semilinear equation Δu=f(x, u), xεΩ (*) where Ω is the complement of some ball in ℝn and f is continuous and nonlinear in u. If, for large x, f is nearly radially symmetric in x, we give conditions under which each positive solution of (*) is asymptotic, as |x|→∞, to some radially symmetric function. Our results can also be useful when f is only bounded above or below by a function which is radially symmetric in x or when the solution oscillates in sign. Examples when f has power-like growth or exponential growth in the variables x and u usefully illustrate our results. © 1993 Springer-Verlag.
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