A Class Of Hardy-Sobolev Equations Nonexistence Of Positive Solutions

This paper is concerned with the nonexistence results for the2k-order singular partial differential system and the Hardy-Sobolev type integral system Here x∈Rn\{0}. We first establish the equivalence between this integral system and an fractional order partial differential system, which includes the2k-order PDE system above. For the integral system, we prove the nonexistence of the positive solu-tion if either0<pq≤1, or pq>1and holds. Thus, the equivalence implies that the fractional order PDE systems, particularly the higher integer-order PDE system, also have no any positive solution. In addition, we give the existence result for the integral system with some double bounded coefficients c1(x)and c2(x) under the condition...