Existence and multiplicity for perturbations of an equation involving Hardy inequality and critical Sobolev exponent in the whole Rⁿ

الأصل · EN

In order to obtain solutions to problem arrayc -Δu=A+h(x)/|x|²u+k(x)u²*⁻¹, x∈ Rⁿ, u>0 inRⁿ, andu∈ D¹,²(Rⁿ), array. h and k must be chosen taking into account not only the size of some norm but the shape. Moreover, if h(x)≡ 0, to reach multiplicity of solution, some hypotheses about the local behaviour of k close to the points of maximum are needed.