Related papers: Using the critical set to induce bifurcations
We present a global bifurcation result for critical values of $C^1$ maps in Banach spaces. The approach is topological based on homotopy equivalence of pairs of topological spaces. For $C^2$ maps, we prove a particular global bifurcation…
We establish a series of concentration and oscillation estimates for elliptic equations with exponential nonlinearity $e^{u^p}$ in a disc. Especially, we show various new results on the supercritical case $p>2$ which are left open in the…
In this paper, we introduce a new class of subsets of bounded linear operators between Banach spaces which is p-version of the uniformly completely continuous sets. Then, we study the relationship between these sets with the equicompact…
This paper improves the algorithms based on supporting halfspaces and quadratic programming for convex set intersection problems in our earlier paper in several directions. First, we give conditions so that much smaller quadratic programs…
We characterize the class of separable Banach spaces $X$ such that for every continuous function $f:X\to\mathbb{R}$ and for every continuous function $\epsilon:X\to\mathbb(0,+\infty)$ there exists a $C^1$ smooth function $g:X\to\mathbb{R}$…
In this paper, we introduce a class of backward stochastic equations (BSEs) that extend classical BSDEs and include many interesting examples of generalized BSDEs as well as semimartingale backward equations. We show that a BSE can be…
A strong inspiration for studying Sobolev type fractional evolution equations comes from the fact that have been verified to be useful tools in the modeling of many physical processes. We introduce a novel technique for solving Sobolev type…
Whenever a clinician reflects on the efficacy of a sequence of treatment decisions for a patient, they may try to identify critical time steps where, had they made different decisions, the patient's health would have improved. While recent…
An equation containing a fractional power of an elliptic operator of second order is studied for Dirichlet boundary conditions. Finite difference approximations in space are employed. The proposed numerical algorithm is based on solving an…
In this note, we show that if a Banach space X has a predual, then every bounded linear operator on X with a continuous functional calculus admits a bounded Borel functional calculus. A consequence of this is that on such a Banach space,…
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…
Plotting solution sets for particular equations may be complicated by the existence of turning points. Here we describe an algorithm which not only overcomes such problematic points, but does so in the most general of settings. Applications…
Considering the large number of fractional operators that exist, and since it does not seem that their number will stop increasing soon at the time of writing this paper, it is presented for the first time, as far as the authors know, a…
We study the extragradient method for solving vector quasi-equilibrium problems in Banach spaces, which generalizes the extragradient method for vector equilibrium problems and scalar quasi-equilibrium problems. We propose a regularization…
The relative equilibria of a symmetric Hamiltonian dynamical system are the critical points of the so-called augmented Hamiltonian. The underlying geometric structure of the system is used to decompose the critical point equations and…
Upper semicontinuous (usc) functions arise in the analysis of maximization problems, distributionally robust optimization, and function identification, which includes many problems of nonparametric statistics. We establish that every usc…
Existence and uniqueness as well as the iterative approximation of fixed points of enriched almost contractions in Banach spaces are studied. The obtained results are generalizations of the great majority of metric fixed point theorems, in…
Let $f:\mathbb{R}^n \to \mathbb{R}$ be a continuously differentiable convex function with its minimizer denoted by $x_*$ and optimal value $f_* = f(x_*)$. Optimization algorithms such as the gradient descent method can often be interpreted…
Given a quasi-smooth Berkovich curve $X$ admitting a finite triangulation, finitely many disjoint open annuli $A_1,\dots,A_n$ in $X$ that are not precompact, and for each $i=1,\dots, n$, an analytic function $f_i$ (resp. differential form…
Using methods from symplectic geometry, the second and fifth authors have provided theoretical groundwork and tools aimed at analyzing periodic orbits, their stability and their bifurcations in families, for the purpose of space mission…