The aim of the paper is to study the properties of positive classical solutions to the fractional Laplace equation with the singular term.Using the extension method,we prove the nonexistence and symmetric of solutions...The aim of the paper is to study the properties of positive classical solutions to the fractional Laplace equation with the singular term.Using the extension method,we prove the nonexistence and symmetric of solutions to the singular fractional equation.展开更多
We give the direct method of moving planes for solutions to the conformally invariant fractional power sub Laplace equation on the Heisenberg group.The method is based on four maximum principles derived here.Then symm...We give the direct method of moving planes for solutions to the conformally invariant fractional power sub Laplace equation on the Heisenberg group.The method is based on four maximum principles derived here.Then symmetry and nonexistence of positive cylindrical solutions are proved.展开更多
基金supported by the Key Scientific Research Project of the Colleges and Universities in Henan Province(No.22A110013)the Key Specialized Research and Development Breakthrough Program in Henan Province(No.222102310265)+1 种基金the Natural Science Foundation of Henan Province of China(No.222300420499)the Cultivation Foundation of National Natural Science Foundation of Huanghuai University(No.XKPY-202008).
文摘The aim of the paper is to study the properties of positive classical solutions to the fractional Laplace equation with the singular term.Using the extension method,we prove the nonexistence and symmetric of solutions to the singular fractional equation.
基金supported by the National Natural Science Foundation of China(No.11771354)。
文摘We give the direct method of moving planes for solutions to the conformally invariant fractional power sub Laplace equation on the Heisenberg group.The method is based on four maximum principles derived here.Then symmetry and nonexistence of positive cylindrical solutions are proved.
