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Radial symmetry and monotonicity for an integral equation. (English) Zbl 1140.45004
Authors’ summary: We study radial symmetry and monotonicity of positive solutions of an integral equation arising from some higher-order semilinear elliptic equations in the whole space n . Instead of the usual method of moving planes, we use a new Hardy-Littlewood-Sobolev type inequality for the Bessel potentials to establish the radial symmetry and monotonicity results.
MSC:
45E10Integral equations of the convolution type
35J65Nonlinear boundary value problems for linear elliptic equations
45M20Positive solutions of integral equations
35C15Integral representations of solutions of PDE
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