Related papers: Laplace-Beltrami operator and exact solutions for …
The method of solving the Bethe-Salpeter equation in Minkowski space, which we developed previously for spinless particles, is extended to a system of two fermions. The method is based on the Nakanishi integral representation of the…
In this paper we consider $(n+1)$-dimensional cosmological model with scalar field and antisymmetric $(p+2)$-form. Using an electric composite $Sp$-brane ansatz the field equations for the original system reduce to the equations for a…
We develop a finite element method for the Laplace-Beltrami operator on a surface with boundary and nonhomogeneous Dirichlet boundary conditions. The method is based on a triangulation of the surface and the boundary conditions are enforced…
The covariant field equations of ten-dimensional super D-branes are obtained by considering fundamental strings whose ends lie in the superworldsurface of the D-brane. By considering in a similar fashion Dp-branes ending on D(p+2)-branes we…
A five-dimensional solution to Einstein's equations coupled to a scalar field has been proposed as a partial solution to the cosmological constant problem: the effect of arbitrary vacuum energy (tension) of a 3-brane is cancelled; however,…
In this paper, we propose an existence result pertaining to a nontrivial solution to the problem \begin{align*} \Bigg\{\begin{split} & \Delta^2_p u -\Delta_p u + \lambda V(x)|u|^{p-2}u = f(x,u)\,,\,x\in \mathbb{R}^N, & u \in…
We prove a result of existence of positive solutions of the Dirichlet problem for $-\Delta_p u=\mathrm{w}(x)f(u,\nabla u)$ in a bounded domain $\Omega\subset\mathbb{R}^N$, where $\Delta_p$ is the $p$-Laplacian and $\mathrm{w}$ is a weight…
In this short letter we present a some rigorous vacuum solutions of the D-dimensional Jordan-Brans-Dicke field equations. In contrast with the well known Brans-Dicke solutions, to the search of static and spherically symmetric space-time we…
In this note, we apply a special metric ansatz to simplify the equations of motion for gravitational systems. Then we construct charged brane solutions in $D=n+p+2$ dimensions which have spherical symmetry of $S^n$ and translational…
We obtain a criterion for the existence of solutions of the problem $$ \Delta_p u = 0 \quad \mbox{in } M \setminus \partial M, \quad \left. u \right|_{ \partial M } = h, $$ with the bounded Dirichlet integral, where $M$ is an oriented…
We study sharp conditions for the existence and nonexistence of infinitely many nonnegative solutions to the problem $-\Delta_p u = \lambda f(u)$ in a bounded domain with Dirichlet boundary conditions, where $f$ is a continuous function…
The Laplace-Beltrami operator on (the surface of) a triaxial ellipsoid admits a sequence of real eigenvalues diverging to plus infinity. By introducing ellipsoidal coordinates, this eigenvalue problem for a partial differential operator is…
The supergravity solutions to various $p$-branes are presented and typically it breaks one quarter of supersymmetry except for the D1 brane case, where it breaks one half of supersymmetry and are manifestly non-relativistic in nature. The…
We present a generic Lagrangian, in arbitrary spacetime dimension $D$, describing the interaction of a dilaton, a graviton and an antisymmetric tensor of arbitrary rank $d$. For each $D$~and~$d$, we find ``solitonic'' black…
We give necessary and sufficient conditions for the existence of weak solutions to the model equation $$-\Delta_p u=\sigma \, u^q \quad \text{on} \, \, \, \R^n,$$ in the case $0<q<p-1$, where $\sigma\ge 0$ is an arbitrary locally integrable…
We investigate the following fractional $p$-Laplacian equation \[ \begin{cases} \begin{aligned} (-\Delta)_p^s u&=\lambda |u|^{q-2}u+|u|^{p_s^*-2}u &&\text{in}~\Omega,\\ u &=0 &&\text{in}~ \mathbb{R}^n\setminus\Omega, \end{aligned}…
We study the effect of non-Abelian T-duality (NATD) on D-brane solutions of type II supergravity. Knowledge of the full interpolating brane solution allows us to track the brane charges and the corresponding brane configurations, thus…
We study cosmological solutions in the dilatonic brane world models. The effective four-dimensional equations on the brane are analyzed for the models with one positive tension brane and two branes with tensions of opposite signs. Just as…
This paper studies a class of $p$-Laplace equations with cubic polynomial nonlinearity \[ \Delta_p v + (v-a_1)(v-a_2)(v-a_3) = 0 \] on complete Riemannian manifolds $M$ with lower Ricci curvature bounds, where $a_1 < a_2 < a_3$ are real…
We discuss the computation of the leading corrections to D-brane solutions due to higher derivative terms in the corresponding low energy effective action. We develop several alternative methods for analyzing the problem. In particular, we…