Symmetric solution 6 Radially symmetric solution 4 Asymmetric profile 2 Asymmetric state 2 Asymptotic behaviors 2 Best constant 2 Best constants 2 BiLaplacian 2 Blow-up 2 Bose-Einstein 2 Bosons 2 Boundary conditions 2 Continuum mechanics 2 Convergence to equilibrium 2 Degree theory 2 Density functional theory 2 Density profile 2 Diffusion 2 Entropy functional 2 Entropy method 2 Entropy methods 2 Fluorine containing polymers 2 Fokker Planck equation 2 Grand canonical ensemble 2 Hopf-cole transformations 2 Initial conditions 2 Invariance under isometries 2 Landesman-Lazer condition 2 Landesman-Lazer conditions 2 Left-right symmetry 2