3 problems

Let $d_0$ and $d_\infty$ be the local degrees of the critical fixed points at $0$ and $\infty$, respectively, and let $\{F_c\}_{c\in\mathbb{C}^*}$ be the one-parameter family of ra…

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…