Multiple solutions for inhomogeneous elliptic problems involving critical Sobolev–Hardy exponents Original Research Article

Let Ω⊂RNΩ⊂RN be a smooth bounded domain such that 0∈Ω0∈Ω, N⩾3N⩾3, 0⩽s<20⩽s<2, 2*(s):=2(N-s)/N-22*(s):=2(N-s)/N-2 is the critical Sobolev–Hardy exponent, f(x)f(x) is a given function. By using the Ekelandʹs variational principle and the mountain pass lemma, we prove the existence of multiple solutions for the singular critical inhomogeneous problem View the MathML source-Δu-μu|x|2=|u|2*(s)-2|x|su+λu+f(x) Turn MathJax on with Dirichlet boundary condition on ∂Ω∂Ω under some assumptions on f(x)f(x), λλ and μμ.