Nonexistence of radial node solutions for elliptic problems with critical Sobolev exponents

Let Ω⊂RnΩ⊂Rn be a ball centered at the origin with radius 1 and 3≤n≤6,2∗=2nn−2 and μ∈[0,(n−22)2). By using a well-known Pohozaev-type identity and some ODE techniques, we obtained the nonexistence of sign-changing radial solutions for elliptic problems with critical Sobolev and Hardy terms −Δu=μ|x|2u+|u|2∗−2u+λuon Ω,u∈H01(Ω) for suitable small positive number λλ. Meanwhile, the nonexistence of radial sign-changing solutions for pp-Laplace problems with critical Sobolev exponent is also obtained.