5 problems

Let $a\in L^{\infty}(0,T)$ satisfy the assumptions in (hp-a), and let $\gamma\in\mathbb{R}\setminus\{-1,0,1\}$. Consider the Neumann and periodic boundary value problems associated…

Gómez-Reñasco–López-Gómez conjecture. There exists $\lambda_c<pi^2$ such that, for every $\lambda<\lambda_c$, the problem admits at least $2^{n+1}-1$ positive solutions.

Case VIII bifurcation conjecture. The branches of solutions to … .

Let $Q'(u)=0$ be the p-Laplacian type equation in a domain $\Omega$, let $\zeta\in\{0,\infty\}$ be an isolated singular point, and let $\mathcal{G}_\zeta$ denote the germs of posit…

Let $1<p<\infty$, let $Q_V$ be the functional under consideration on a domain $\Omega$, and let $\Omega_1\Subset\Omega$ be a smooth open set. Denote by…