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Boundary control problems with convex cost and dynamic programming in infinite dimension part II: Existence for HJB
Qualitative properties of solutions for an integral equation
1.  Department of Mathematics, Yeshiva University, 500 W 185th Street, New York, NY 10033, United States 
2.  Department of Applied Mathematics, University of Colorado at Boulder 
3.  Department of Mathematics, University of Toledo, Toledo OH 43606 
$ u(x) = \int_{R^n} \frac{1}{xy^{n\alpha}} K(y) u(y)^p dy.
We establish regularity, radial symmetry, and monotonicity of the solutions. We also consider subcritical cases, super critical cases, and singular solutions in all cases; and obtain qualitative properties for these solutions.
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