相关论文: A degree theory approach for the shooting method

The characterization of systems of differential equations admitting a superposition function allowing us to write the general solution in terms of any fundamental set of particular solutions is discussed. These systems are shown to be…

This paper describes a method of global localization based on graph-theoretic association of instances between a query and the prior map. The proposed framework employs correspondence matching based on the maximum clique problem (MCP). The…

In this paper we prove the global existence of classical static solutions of Einstein gravitational theory coupled to a real scalar field where the spacetime admits spherically symmetry. The equations of motions can then be reduced into a…

Linear response theory is a tool with which one can study systems that are driven out of equilibrium by external perturbations. This monograph presents a thoroughly modern framework to make linear response theory rigorous for a wide array…

The graduated optimization approach, also known as the continuation method, is a popular heuristic to solving non-convex problems that has received renewed interest over the last decade. Despite its popularity, very little is known in terms…

The presence of symmetries in a Hamiltonian system usually implies the existence of conservation laws that are represented mathematically in terms of the dynamical preservation of the level sets of a momentum mapping. The symplectic or…

Classical energy-momentum methods study the existence and stability properties of solutions of $t$-dependent Hamilton equations on symplectic manifolds whose evolution is given by their Hamiltonian Lie symmetries. The points of such…

In this paper, we study the existence and qualitative properties of positive solutions to a Choquard-type equation with Hardy potential. We develop a nonlocal version of concentration-compactness principle involving the Hardy potential to…

In the classical binary search in a path the aim is to detect an unknown target by asking as few queries as possible, where each query reveals the direction to the target. This binary search algorithm has been recently extended by…

Despite the breakthroughs achieved by deep learning models in conventional supervised learning scenarios, their dependence on sufficient labeled training data in each class prevents effective applications of these deep models in situations…

In this paper we prove the existence and the multiplicity of radial positive oscillatory solutions for a nonlinear problem governed by the mean curvature operator in the Lorentz-Minkowski space. The problem is set in a ball $B_R$ of…

Classical guidance laws aim at minimizing the miss distance, thus implicitly determining the minimum warhead lethality radius required against nominal targets. However, nonnominal targets or scenarios might render the designed warhead…

Improved local and global versions of the effective Nullstellensatz for ideal sheaves on non-singular complex varieties are obtained, based on a new invariant motivated by the notion of finite type from the theory of several complex…

Randomly initialized first-order optimization algorithms are the method of choice for solving many high-dimensional nonconvex problems in machine learning, yet general theoretical guarantees cannot rule out convergence to critical points of…

Low-shot counters estimate the number of objects corresponding to a selected category, based on only few or no exemplars annotated in the image. The current state-of-the-art estimates the total counts as the sum over the object location…

In this paper, we study some qualitative properties of Hardy-Littlewood-Sobolev type systems. The HLS type systems are categorized into three cases: critical, supercritical and subcritical. The critical case, the well known original HLS…

In this paper we study a class of Hardy--Sobolev type systems defined in $\mathbb{R}^N$ and coupled by a singular critical Hardy--Sobolev term. The main novelty of this work is that the orders of the singularities are independent and…

In this article we are concern for the following Choquard equation \[ -\Delta u = \lambda |u|^{q-2}u +\left(\int_\Omega \frac{|u(y)|^{2^*_\mu}}{|x-y|^\mu} dy \right)|u|^{2^*_\mu-2} u \; \text{in}\; \Omega,\quad u = 0 \; \text{ on } \partial…

In this article we develop a convergence theory for goal-oriented adaptive finite element algorithms designed for a class of second-order semilinear elliptic equations. We briefly discuss the target problem class, and introduce several…

This paper aims to provide a careful and self-contained introduction to the theory of topological degree in Euclidean spaces. It is intended for people mostly interested in analysis and, in general, a heavy background in algebraic or…