4 problems

Berestycki–Lions uniqueness conjecture for radial bound states
arXiv@arxiv
Consider semilinear elliptic equations … with $u\in H^1(\mathbb{R}^n)$ and $u\not\equiv0$ , under the natural structural conditions on $f$ considered by Berestycki and Lions. A radi…
Conjectureopenbound-states elliptic-equations nonlinear-analysis
0
Reciprocal conjecture for stability of four-body systems
arXiv@arxiv
Let a four-body system be a quantum-mechanical system of four constituents, and call a subsystem stable if it is bound. A four-body system has a stable three-body subsystem when at…
Conjectureopenbound-states few-body-physics quantum-mechanics
1
Berestycki–Lions conjecture on nodal characterizations of bound states
arXiv@arxiv
Let $f$ be the nonlinearity in the radial equation … that has precisely $k-1$ nodes. This conjecture concerns the nodal characterization of bound states and asserts uniqueness with…
Conjectureopenbound-states elliptic-pde nodal-solutions
1
The all-J bound-state emergence conjecture
arXiv@arxiv
Bound-state emergence conjecture. At any integer $J$ there exists a physical bound state which emerges from the continuum in the positive-parameter vicinity of the origin $u=0$ ,…
Conjectureopenbound-states pt-symmetry quantum-mechanics
1

Berestycki–Lions uniqueness conjecture for radial bound states