相关论文: Ground state solution for a problem with mean curv…
We solve the inverse spectral problem for rotationally symmetric manifolds, which include the class of surfaces of revolution, by giving an analytic isomorphism from the space of spectral data onto the space of functions describing the…
Focusing on the fourth-order wave equation $u_{tt} + \Delta^2 u + f(u)= 0$, we prove the existence of ground state solutions $u=u(x+ct)$ for an optimal range of speeds $c\in\mathbb{R}^n$ and a variety of nonlinearities $f$.
In this paper, we study the existence of normalized ground state solutions for the following biharmonic Choquard system \begin{align*} \begin{split} \left\{ \begin{array}{ll} \Delta^2u=\lambda_1 u+(I_\mu*F(u,v))F_u (u,v), \quad\mbox{in}\ \…
We consider the nonlinear wave equation, with a large exponent, power-like non-linearity, outside a ball of the Euclidean 3-dimensional space. In a previous article, we have proved that any global solution converges, up to a radiation term,…
In the present paper, we study timelike surfaces with parallel normalized mean curvature vector field in the four-dimensional Minkowski space. We introduce special isotropic parameters on each such surface, which we call canonical…
This paper is mainly concerned with the existence of ground state sign-changing solutions for a class of second order quasilinear elliptic equations in bounded domains which derived from nonlinear optics models. Combining a non-Nehari…
We prove the existence of a pair of positive radial solutions for the Neumann boundary value problem \begin{equation*} \begin{cases} \, \mathrm{div}\,\Biggl{(} \dfrac{\nabla u}{\sqrt{1- | \nabla u |^{2}}}\Biggr{)} + \lambda a(|x|)u^p = 0, &…
The paper studies a regularization of the quantum (effective) action for a scalar field theory in a general position on a compact smooth Riemannian manifold. As the main method, we propose the use of a special averaging operator, which…
In this paper we present in detail the numerical solution of the conformally invariant wave equation on top of a fixed background space-time corresponding to two different cases: i) 1+1 Minkowski space-time in Cartesian coordinates and ii)…
We prove an existence theorem for positive solutions to Lichnerowicz-type equations on complete manifolds with boundary and nonlinear Neumann conditions. This kind of nonlinear problems arise quite naturally in the study of solutions for…
In this paper, we consider Kirchhoff-Schrodinger equations with singular exponential nonlinearities in R^4,using singular Adams inequality and variational techniques, we get the existence of ground state solutions. Moreover, we also get the…
By using a shooting technique, we prove that the quasilinear boundary value problem $$ \textrm{div} \, \left( \frac{\nabla u}{\sqrt{1-| \nabla u |^2}}\right) + \lambda q(| x |) | u |^{p-1} u = 0, \qquad u|_{\partial \mathcal{B}} = 0,$$…
We construct solutions of the Cahn-Hilliard equation whose nodal set converges to a given constant mean curvature hypersurface in a Riemannian manifold.
In this paper, the ground state Wigner function of a many-body system is explored theoretically and numerically. First, an eigenvalue problem for Wigner function is derived based on the energy operator of the system. The validity of finding…
We prove that any regular domain in Minkowski space is uniquely foliated by spacelike constant mean curvature (CMC) hypersurfaces. This completes the classification of entire spacelike CMC hypersurfaces in Minkowski space initiated by Choi…
In this paper we address the existence and uniqueness of entire spacelike hypersurfaces in the Lorentz--Minkowski space $\mathbb{L}^{m+1}$ with prescribed mean curvature that are star-shaped with respect to a point and asymptotic to a light…
We study an area minimization problem for spacelike zero mean curvature surfaces in four dimensional Lorentz-Minkowski space. The areas of these surfaces are compared of with the areas of certain marginally trapped surfaces having the same…
We prove an existence result for non rotational constant mean curvature ends in $\mathbb{H}^2 \times \mathbb{R}$, where $\mathbb{H}^2$ is the hyperbolic real plane. The value of the curvature is $h \, \in \, (0, 1/2)$. We use Schauder…
The Bethe-Salpeter equation (BSE) for bound states in scalar theories is reformulated and solved in terms of a generalized spectral representation directly in Minkowski space. This differs from the conventional approach, where the BSE is…
We consider prescribed mean curvature equations whose solutions are minimal surfaces, constant mean curvature surfaces, or capillary surfaces. We consider both Dirichlet boundary conditions for Plateau problems and nonlinear Neumann…