Abstract
For 0 n/(n − m), we study the inhomogeneous equation Lu+up + V (x)u + f(x) = 0 in ℝn with singular data f and V. The symbol σ of the operator L is bounded from below by |ξ|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 σ, 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.
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