科研之友
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摘要
For 0 < m < n, p a positive integer and p > n/(n - m), we study the inhomogeneous equation L (u) +u (p) + V (x)u + f(x) = 0 in a"e (n) with singular data f and V. The symbol sigma of the operator L is bounded from below by |xi| (m) . Examples of L are Laplacian, biharmonic and fractional order operators. Here f and V can have infinite singular points, change sign, oscillate at infinity, and be measures. Also, f and V can blow up on an unbounded (n-1)-manifold. The solution u can change sign, be nonradial and singular. If sigma, f and V are radial, then u is radial. The assumptions on f and V are in terms of their Fourier transforms and we provide some examples.
- 出版日期2013-1
