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- W2101219122 abstract "For several classes of functions including the special case f(u) = u p 1 u m , m > p 1 > 0, we obtain Liouville type, boundedness and symme- try results for solutions of the non-linear p-Laplacian problem pu = f(u) defined on the whole space Rn. Suppose u 2 C2(Rn) is a solution. We have that either (1) if u doesn't change sign, then u is a constant (hence, u 1 or u 0 or u 1); or (2) if u changes sign, then u 2 L1(Rn), moreover |u| 0 on Rn and the level set u 1(0) lies on one side of a hyperplane and touches that hyperplane, i.e., there exists 2 S n 1 and x0 2 u 1 (0) such that · (x x0) 0 for all x 2 u 1 (0), then u depends on one variable only (in the direction of )." @default.
- W2101219122 created "2016-06-24" @default.
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- W2101219122 date "2003-09-25" @default.
- W2101219122 modified "2023-09-24" @default.
- W2101219122 title "Qualitative properties of solutions for quasi-linear elliptic equations" @default.
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