Related papers: Ground states of elliptic problems over cones
We study existence and multiplicity of positive radial solutions for a coupled elliptic system in exterior domains where the nonlinearities depend on the gradients and the boundary conditions are nonlocal. We use a non-standard cone to…
We proceed with the study of the Nehari manifold method for functionals in $C^1(X \setminus \{0\})$, where $X$ is a Banach space. We deal now with functionals whose fibering maps have two critical points (a minimiser followed by a…
We consider a skew ruled surface $\Phi$ in the Euclidean space $E^{3}$ and relative normalizations of it, so that the relative normals at each point lie in the corresponding asymptotic plane of $\Phi$. We call such relative normalizations…
The special interest is devoted to such situations when the material space of our object with affine degrees of freedom has generally lower dimension than the one of the physical space. In other words when we have the $m$-dimensional…
Given $k\in\mathbb N$, we define a class of continuous piecewise functions $f$ having abrupt but controlled magnitude changes so that the problem $$\Delta u +f(u)=0,\quad x\in \mathbb R^N, N> 2, $$ has at least $k$ radially symmetric ground…
We shall introduce a stability condition for a coherent sheaf associated to an elliptic surface. Then we study the behavior under relative Fourier-Mukai transforms.
An infinite triangular lattice of classical dipolar spins is usually considered to have a ferromagnetic ground state. We examine the validity of this statement for finite lattices and in the limit of large lattices. We find that the ground…
We show that the ground state interface geometry of binary condensates in the phase separated regime undergoes a smooth transition from planar to ellipsoidal to cylindrical geometry. This occurs for condensates with repulsive interactions…
In this paper we study $\varphi$-minimal surfaces in $\mathbb{R}^3$ when the function $\varphi$ is invariant under a two-parametric group of translations. Particularly those which are complete graphs over domains in $\mathbb{R}^2$. We…
We extend the well-known Gelfand-Phillips property for Banach spaces to locally convex spaces, defining a locally convex space $E$ to be Gelfand-Phillips if every limited set in $E$ is precompact in the topology on $E$ defined by barrels.…
It is established some existence and multiplicity of solution results for a quasilinear elliptic problem driven by $\Phi$-Laplacian operator. One of these solutions is built as a ground state solution. In order to prove our main results we…
On each nonreflexive Banach space X there exists a positive continuous convex function f such that 1/f is not a d.c. function (i.e., a difference of two continuous convex functions). This result together with known ones implies that X is…
In this paper, given a reflexive real Banach space X and two sequentially weakly lower semicontinuous functionals Phi, Psi on X with Psi strongly continuous and coercive, we are mainly interested in the existence of infinitely many local…
It is established ground states and multiplicity of solutions for a nonlocal Schr\"{o}dinger equation $(-\Delta )^s u + V(x) u = \lambda a(x) |u|^{q-2}u + b(x)f(u)$ in $\mathbb{R}^N,$ $u \in H^s(\mathbb{R}^N),$ where $0<s<\min\{1,N/2\},$…
We consider limits of equilibrium distributions as temperature approaches zero, for systems of infinitely many particles, and characterize the support of the limiting distributions. Such results are known for particles with positions on a…
The prospect of realizing highly entangled states on quantum processors with fundamentally different hardware geometries raises the question: to what extent does a state of a quantum spin system have an intrinsic geometry? In this paper, we…
In this paper, we study the ordinarity of an isotrivial elliptic surface defined over a field of positive characteristic. If an isotrivial elliptic fibration $\pi:X \to C$ is given, $X$ is ordinary when the common fiber of $\pi$ is ordinary…
The aim of the present paper is essentially to prove that if $\Phi$ and $\Psi$ are two sequentially weakly lower semicontinuous functionals on a reflexive real Banach space and if $\Psi$ is also continuous and coercive, then then following…
We consider the Dirichlet problem for second-order elliptic systems with constant coefficients. We prove that non-reducible strongly elliptic systems of this type do not admits non-negatively defined energy functionals of the form…
We consider the translationally invariant Pauli-Fierz model describing a charged particle interacting with the electromagnetic field. We show under natural assumptions that the fiber Hamiltonian at zero momentum has a ground state.