Entire solutions of quasilinear elliptic equations |
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Authors: | James Serrin |
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Institution: | School of Mathematics, University of Minnesota, Minneapolis, MN, United States |
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Abstract: | We study entire solutions of non-homogeneous quasilinear elliptic equations, with Eqs. (1) and (2) below being typical. A particular special case of interest is the following: Let u be an entire distribution solution of the equation Δpu=|u|q−1u, where p>1. If q>p−1 then u≡0. On the other hand, if 0<q<p−1 and u(x)=o(|x|p/(p−q−1)) as |x|→∞, then again u≡0. If q=p−1 then u≡0 for all solutions with at most algebraic growth at infinity. |
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Keywords: | Elliptic differential equations Entire solutions Liouville theorems |
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