Recursos de colección
Project Euclid (Hosted at Cornell University Library) (191.996 recursos)
Topological Methods in Nonlinear Analysis
Topological Methods in Nonlinear Analysis
Xia, Shengxiang; Yin, Yanmin
We utilize the methods of computational topology to the
database of optical flow created by Roth and Black from range images, and demonstrate
a qualitative topological analysis of spaces of $3 \times 3, 5 \times 5$ and
$7 \times 7$ optical flow patches. We experimentally prove that there exist
subspaces of the spaces of the three sizes high-contrast patches that are
topologically equivalent to a circle and a three circles model, respectively.
The Klein bottle is the quotient space described as the square $[0,1] \times [0,1]$
with sides identified by the relations $(0, y)\sim (1, y)$ for $y\in [0, 1]$ and
$(x, 0) \sim (1-x, 1)$ for $...
Bugajewska, Daria; Bugajewski, Dariusz; Kasprzak, Piotr; Maćkowiak, Piotr
The main goal of this paper is to give an answer to the main
problem of the theory of nonautonomous superposition operators
acting in the space of functions of bounded variation in the
sense of Jordan. Namely, we give necessary and sufficient
conditions which guarantee that nonautonomous superposition
operators map that space into itself and are locally bounded.
Moreover, special attention is drawn to nonautonomous
superposition operators generated by locally bounded mappings as
well as to superposition operators generated by functions with
separable variables.
Benedetti, Irene; Väth, Martin
An existence result for an abstract nonlocal boundary value
problem $x'\in A(t)x(t)+F(t,x(t))$, $Lx\in B(x)$, is given, where
$A(t)$ determines a linear evolution operator, $L$ is linear, and
$F$ and $B$ are multivalued. To avoid compactness conditions, the
weak topology is employed. The result applies also in nonreflexive
spaces under a hypothesis concerning the De Blasi measure of
noncompactness. Even in the case of initial value problems,
the required condition is essentially milder than previously known
results.
Vrabie, Ioan I.
The goal of this paper is to show that some classes of partial
differential functional equations admit a natural formulation as
ordinary functional differential equations in infinite dimensional
Banach spaces. Moreover, the equations thus obtained are
driven by continuous right-hand sides satisfying the compactness
assumptions required by the infinite-dimensional version of a
Peano-like existence theorem. Two applications, one to a
semilinear wave equation with delay and another one to a
pseudoparabolic PDE in Mechanics, are included.
Guedda, Lahcene
In this paper we study the topological structure of the solution
set of abstract inclusions, not necessarily linear, with infinite
delay on a Banach space defined axiomatically. By using the
techniques of the theory of condensing maps and multivalued
analysis tools, we prove that the solution set is a compact
$R_\delta$-set. Our approach makes possible to give a unified
scheme in the investigation of the structure of the solution set
of certain classes of differential inclusions with infinite delay.
Radul, Taras
This paper is devoted to Nash equilibrium for games in
capacities. Such games with payoff expressed by the Choquet
integral were considered by Kozhan and Zarichnyi (2008) and
existence of Nash equilibrium was proved. We also consider games
in capacities but with expected payoff expressed by the Sugeno
integral. We prove existence of Nash equilibrium in a general
context of abstract binary (non-linear) convexity and then we
obtain an existence theorem for games in capacities.
Zhang, Liang; Tang, Xianhua; Chen, Yi
In this paper, we study the existence of infinitely many solutions for the
quasilinear Schrödinger equations
$$
\begin{cases}
-\Delta u-\Delta(|u|^{\alpha})|u|^{\alpha-2}u=g(x,u)+h(x,u) &\text{for } x\in \Omega,\\
u=0 &\text{for } x\in \partial\Omega,
\end{cases}
$$
where $\alpha\geq 2$, $g, h\in C(\Omega\times \mathbb{R}, \mathbb{R})$. When $g$
is of superlinear growth at infinity in $u$ and $h$ is not odd in
$u$, the existence of infinitely many solutions is proved in spite
of the lack of the symmetry of this problem, by using the dual
approach and Rabinowitz perturbation method. Our results
generalize some known results and are new even in the symmetric
situation.
Walther, Hans-Otto
We construct a semiflow of continuously differentiable solution
operators for delay differential equations $x'(t)=f(x_t)$ with $f$
defined on an open subset of the Fréchet space
$C^1=C^1((-\infty,0],\mathbb{R}^n)$. This space has the advantage
that it contains all histories $x_t=x(t+\cdot)$, $t\in\mathbb R$, of
every possible entire solution of the delay differential equation,
in contrast to a Banach space of maps $(-\infty,0]\to\mathbb R^n$ whose
norm would impose growth conditions at $-\infty$. The semiflow
lives on the set $X_f=\{\phi\in U:\phi'(0)=f(\phi)\}$ which is a
submanifold of finite codimension in $C^1$. The hypotheses are
that the functional $f$ is continuously differentiable (in the
Michal-Bastiani sense) and that the derivatives have a mild
extension property. The result applies to autonomous...
Gasull, Armengol; Groisman, Jorge; Mañosas, Francesc
Kerékjártó proved in 1934 that a planar homeomorphism with an asymptotically stable fixed point
is conjugated, on its basin of attraction, to one of the maps $z\mapsto z/2$ or $z\mapsto \overline z/2$,
depending on whether $f$ preserves or reverses the orientation. We extend this result to planar
homeomorphisms with a compact attractor.
do Ó, João Marcos; Miyagaki, Olímpio H.; Squassina, Marco
We investigate the existence of ground state solutions for a class
of nonlinear scalar field equations defined on the whole real
line, involving a fractional Laplacian and nonlinearities with
Trudinger-Moser critical growth. We handle the lack of
compactness of the associated energy functional due to the
unboundedness of the domain and the presence of a limiting case
embedding.
Amster, Pablo; Haddad, Julián
We prove existence and multiplicity of periodic motions for the
forced $2$-body problem under conditions of topological character.
In different cases, the lower bounds obtained for the number of
solutions are related to the winding number of a curve in the
plane and the homology of a space in $\mathbb R^3$.
Mai, Jiehua; Sun, Taixiang
Let $I$ be a bounded connected subset of $ \mathbb{R}$ containing more than one point,
and $\mathcal L(I)$ be the family of all nonempty connected
subsets of $I$. Each map from $I$ to $\mathcal L(I)$ is called
a multivalued map. A multivalued map
$F\colon I\rightarrow\mathcal L(I)$ is called a multivalued map
with continuous margins if both the left endpoint and
the right endpoint functions of $F$ are continuous. We show that the well-known Sharkovskiĭ theorem for interval
maps also holds for every multivalued map
with continuous margins $F\colon I\rightarrow \mathcal L(I)$,
that is, if $F$ has an $n$-periodic orbit and $n\succ m$ (in the
Sharkovskiĭ ordering), then $F$ also has...
González, Jesús; Gutiérrez, Bárbara; Yuzvinsky, Sergey
We construct "higher" motion planners for automated systems
whose spaces of states are homotopy equivalent to a polyhedral
product space $Z(K,\{(S^{k_i},\star)\})$, e.g. robot arms with
restrictions on the possible combinations of simultaneously moving
nodes. Our construction is shown to be optimal by explicit
cohomology calculations. The higher topological complexity of
other families of polyhedral product spaces is also determined.
Ye, Hongyu
In this paper, we study the existence of minimizers to the
following functional related to the nonlinear Choquard equation:
$$
E(u)=\frac{1}{2}\int_{\mathbb R^N}|\nabla
u|^2+\frac{1}{2}\int_{\mathbb R^N}V(x)|u|^2
-\frac{1}{2p}\int_{\mathbb R^N}(I_\alpha*|u|^p)|u|^p
$$
on $\widetilde{S}(c)=\{u\in H^1(\mathbb R^N)\mid
\int_{\mathbb R^N}V(x)|u|^2< +\infty, \, |u|_2=c,\, c> 0\}$, where $N\geq 1$,
$\alpha\in(0,N)$, $({N+\alpha})/{N}\leq p< (N+\alpha)/(N-2)_+$ and
$I_\alpha\colon \mathbb R^N\rightarrow\mathbb R$ is the Riesz potential. We present
sharp existence results for $E(u)$ constrained on
$\widetilde{S}(c)$ when $V(x)\equiv0$ for all
$(N+\alpha)/N\leq p< (N+\alpha)/(N-2)_+$. For the mass
critical case $p=(N+\alpha+2)/N$, we show that if $0\leq V\in
L_{\rm loc}^{\infty}(\mathbb R^N)$ and
$\lim\limits_{|x|\rightarrow+\infty}V(x)=+\infty$, then mass
minimizers exist only if $0< c< c_*=|Q|_2$ and concentrate at the
flattest minimum of $V$ as $c$ approaches $c_*$ from below, where
$Q$ is a groundstate solution of $-\Delta
u+u=(I_\alpha*|u|^{(N+\alpha+2)/N})|u|^{(N+\alpha+2)/N-2}u$
in...
Burlică, Monica-Dana; Roşu, Daniela
We consider a class of abstract evolution reaction-diffusion systems with delay and nonlocal initial data of the form
$$
\begin{cases}
\displaystyle
u'(t)\in Au(t)+F(t,u_t,v_t)&\text{for } t\in \mathbb{R}_+,\\
v'(t)\in Bv(t)+G(t,u_t,v_t) & \text{for } t\in \mathbb{R}_+,\\
u(t)=p(u,v)(t)& \text{for } t\in [-\tau_1,0],\\
v(t)=q(u,v)(t)& \text{for } t\in [-\tau_2,0],
\end{cases}
$$
where $\tau_i\geq 0$, $i=1,2$, $A$ and $B$ are two $m$-dissipative
operators acting in two Banach spaces, the perturbations $F$ and
$G$ are continuous, while the history functions $p$ and $q$ are
nonexpansive functions with affine growth. We prove an existence
result of $C^0$-solutions for the above problem and we give an
example to illustrate the effectiveness of our abstract theory.
Zhang, Jian; Zou, Wenming
We consider the nonlinear Schrödinger equation
\begin{equation*}
-\Delta u + (1+\mu g(x))u = f(u) \quad \text{in } \mathbb{R}^N,
\end{equation*}
where $N \ge 3$, $\mu \ge 0$; the function $g \ge 0$ has a potential well and $f$
has critical growth. By using variational methods, the
existence and concentration behavior of the ground state solution are obtained.
Kuperberg, Krystyna M.; Kuperberg, Włodzimierz; Minc, Piotr; Reed, Coke S.
Corvellec, Jean-Noël; Degiovanni, Marco; Marzocchi, Marco
Dancer, E.N.
Ben-Naoum, A.K.; Mawhin, J.