The cyclicity of period annuli of some classes of reversible and non-Hamiltonian quadratic systems under quadratic perturbations are studied. The argument principle method and the centroid curve method are combined to prove that the related Abelian integral has at most two zeros.
The non‐uniqueness of solutions of basic Dirichlet‐type problems is a surprising feature of the fractional Laplace equation. This paper establishes a somewhat sharp uniqueness condition for the fractional Laplace equation. We derive the ‐estimate for fractional Laplacian operators to better understand this phenomenon. We introduce several naturally weighted fractional Sobolev spaces and establish embedding relationships among them. These existence‐uniqueness conditions and the spaces we introduce here are intrinsically related to the fractional Laplacian and provide basic information for studying related problems.
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