3 problems

Let $n$ and $k$ satisfy $2k>n$, and let $\kappa=(\kappa_1,\dots,\kappa_n)\in\Gamma_k$, where $\Gamma_k$ is the Gårding cone for the $k$-th elementary symmetric polynomial. Assume t…

Let $\Omega$ be the domain and let $f$ be the nonlinearity in the $k$-Hessian problem … has no nontrivial solution for every $\lambda\in(0,\lambda_{*})$ and at least two nontrivial…

Let $\Omega$ be the domain and let $f$ be the nonlinearity in the $k$-Hessian problem … has at least two convex solutions for every $\lambda>\lambda_{*}$, exactly one convex soluti…