We study the equation $$-\Delta u=\lambda\left(\frac{e^u}{\int_\oep e^u}- \frac{1}{|\oep|}\right)\quad \text{in }\oep$$ for $u\in E$, where $E = \{ u \in H^1(\oep): u \hbox{ is doubly periodic}, \int_{\oep} u = 0 \}$ and ...

We consider positive semistable solutions u of Lu + f(u) = 0 with zero Dirichlet boundary condition, where L is a uniformly elliptic operator and f is an element of C-2 is a positive, nondecreasing, and convex nonlinearity ...

This article concerns the antisymmetry, uniqueness, and monotonicity properties of solutions to some elliptic functionals involving weights and a double well potential. In the one-dimensional case, we introduce the continuous ...

We are concerned with hypersurfaces of RN with constant nonlocal (or fractional) mean curvature. This is the equation associated to critical points of the fractional perimeter under a volume constraint. Our results are ...

We establish sharp energy estimates for some solutions, such as global minimizers, monotone solutions and saddle-shaped solutions, of the fractional nonlinear equation 1/2 in R n. Our energy estimates hold for every ...