Existence of Solutions of a Non-Linear Eigenvalue Problem with a Variable Weight

Rejeb Hadiji, Francois Vigneron

We study the non-linear minimization problem on $H_0^1(\Omega )\subset L^q$ with $q=\frac{2n}{n-2}$, $\alpha >0$ and $n\ge 4$~: \[\inf_{\substack{u\in H^1_0(Ω) \|u\|_{L^q}=1}}\int_Ωa(x,u)|\nab…