Mostrando recursos 1 - 20 de 1.089

  1. On the nonlinear analysis of optical flow

    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 $...

  2. Nonautonomous superposition operators in the spaces of functions of bounded variation

    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.

  3. Semilinear inclusions with nonlocal conditions without compactness in non-reflexive spaces

    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.

  4. A local existence theorem for a class of delay differential equations

    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.

  5. On the structure of the solution set of abstract inclusions with infinite delay in a Banach space

    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.

  6. Nash equilibrium for binary convexities

    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.

  7. Infinitely many solutions for quasilinear Schrödinger equations under broken symmetry situation

    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.

  8. Semiflows for differential equations with locally bounded delay on solution manifolds in the space $C^1((-\infty,0],\mathbb R^n)$

    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...

  9. Linearization of planar homeomorphisms with a compact attractor

    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.

  10. Ground states of nonlocal scalar field equations with Trudinger-Moser critical nonlinearity

    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.

  11. On existence of periodic solutions for Kepler type problems

    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 $\mathbb R^3$.

  12. Periodic orbits for multivalued maps with continuous margins of intervals

    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...

  13. Higher topological complexity of subcomplexes of products of spheres and related polyhedral product spaces

    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.

  14. Mass minimizers and concentration for nonlinear Choquard equations in $\mathbb R^N$

    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...

  15. Nonlinear delay reaction-diffusion systems with nonlocal initial conditions having affine growth

    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.

  16. Existence and concentrate behavior of Schrödinger equations with critical exponential growth in $\mathbb{R}^N$

    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.

  17. Examples related to Ulam's fixed point problem

    Kuperberg, Krystyna M.; Kuperberg, Włodzimierz; Minc, Piotr; Reed, Coke S.

  18. Deformation properties for continuous functionals and critical point theory

    Corvellec, Jean-Noël; Degiovanni, Marco; Marzocchi, Marco

  19. Generic domain dependence for non-smooth equations and the open set problem for jumping nonlinearities

    Dancer, E.N.

  20. Periodic solutions of some semilinear wave equations on balls and on spheres

    Ben-Naoum, A.K.; Mawhin, J.

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