Four solutions of an inhomogeneous elliptic equation with critical exponent and singular term Original Research Article

In this paper, we prove the existence of four nontrivial solutions of View the MathML source−Δu−λ|x|2u=|u|2∗−2u+μ|x|α−2u+f(x),x∈Ω∖{0} Turn MathJax on and show that at least one of them is sign changing. Our results extend some previous works, such as [G. Tarantello, Multiplicity results for an inhomogeneous Neumann problem with critical exponent, Manuscripta Math., 81 (1993) 51–78; D. Kang and Y. Deng, Multiple solutions for inhomogeneous elliptic problems involving critical Sobolev–Hardy exponents, J. Math. Anal. Appl., 60 (2005) 729–753; N. Hirano and N. Shioji, A multiplicty result including a sign changing solution for an inhomogeneous Neumann problem with critical exponent, Proc. Roy. Soc. Edinburgh, 137A (2007) 333–347.