Asymptotic behavior of solutions of nonlinear elliptic equations |
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Authors: | Steven D. Taliaferro |
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Affiliation: | (1) Mathematics Department, Texas A & M University, 77843 College Station, Texas |
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Abstract: | We study and obtain formulas for the asymptotic behavior as ¦x¦ of C2 solutions of the semilinear equation u=f(x, u), x (*) where is the complement of some ball in n 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. |
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