Mostrando recursos 1 - 20 de 194

  1. Boundary Value Problems for Degenerate Coupled Systems with Variable Time Delay

    Bokalo, Mykola; Ilnytska, Olga
    The boundary value problems for coupled systems of parabolic and ordinary differential equations, where all equations contain time depended delay and degenerate at initial moment, are considered. Existence and uniqueness of classical solutions of these problems are proved. A priori estimates are obtained.

  2. Periodic Travelling Waves and its Inter-relation with Solitons for the 2D abc-Boussinesq System

    Quintero, Jose R.; Montes, Alex M.
    Via a variational approach involving Concentration-Compactness principle, we show the existence of $x$-periodic travelling wave solutions for a general 2D-Boussinesq system that arises in the study of the evolution of long water waves with small amplitude in the presence of surface tension. We also establish that $x$-periodic travelling waves have almost the same shape of solitons as the period tends to infinity, by showing that a special sequence of $x$-periodic travelling wave solutions parameterized by the period converges to a solitary wave in a appropriate sense.

  3. Variational Inequality with Evolutional Curl Constraint in a Multi-Connected Domain

    Aramaki, Junichi
    We consider a system of quasilinear parabolic type equations involving operator curl associated with the Maxwell equations in a multi-connected domain. The paper is a continuation of the author's previous paper. We deal with a variational inequality with curl constraint. It is an extension of the results of Miranda et al. for $p$-curl system.

  4. Generalizations of Majorization Inequality via Lidstone's Polynomial and Their Applications

    Khan, M. Adil; Latif, N.; Pecaric, J.
    In this paper, we obtain the generalizations of majorization inequalities by using Lidstone's interpolating polynomials and conditions on Green's functions. We give bounds for identities related to the generalizations of majorization inequalities by using Čebyšev functionals. We also give Grüss type inequalities and Ostrowski-type inequalities for these functionals. We present mean value theorems and $n$-exponential convexity which leads to exponential convexity and then log-convexity for these functionals. We give some families of functions which enable us to construct a large families of functions that are exponentially convex and also give Stolarsky type means with their monotonicity.

  5. Propagation Speed for Fractional Cooperative Systems with Slowly Decaying Initial Conditions

    Yangari, Miguel
    The aim of this paper is to study the time asymptotic propagation for mild solutions to the fractional reaction diffusion cooperative systems when at least one entry of the initial condition decays slower than a power. We state that the solution spreads at least exponentially fast with an exponent depending on the diffusion term and on the smallest index of fractional Laplacians.

  6. Lebedev's Type Index Transforms with the Modified Bessel Functions

    Yakubovich, Semyon
    New index transforms of the Lebedev type are investigated. It involves the real part of the product of the modified Bessel functions as the kernel. Boundedness properties are examined for these operators in the Lebesgue weighted spaces. Inversion theorems are proved. Important particular cases are exhibited. The results are applied to solve an initial value problem for the fourth order PDE, involving the Laplacian. Finally, it is shown that the same PDE has another fundamental solution, which is associated with the generalized Lebedev index transform, involving the square of the modulus of Macdonald's function, recently considered by the author.

  7. A Note on Closedness of the Sum of Two Closed Subspaces in a Banach Space

    Zheng, Zhe-Ming; Ding, Hui-Sheng
    Let $X$ be a Banach space, and $M,N$ be two closed subspaces of $X$. We collect several necessary and sufficient conditions for the closedness of $M+N$ ($M+N$ is not necessarily direct sum), and show that a necessary condition in a classical textbook is also sufficient.

  8. Completeness of Sums of Subspaces of Bounded Functions and Applications

    Blot, Joel; Cieutat, Philippe
    We establish the completeness of spaces of $\mu$-pseudo almost periodic functions (or sequences) and $\mu$-pseudo almost automorphic functions (or sequences) by establishing a new result on the closedness of the sum of closed vector subspaces of the Banach space of bounded functions. To obtain this result we use abstract tools on the closedness of the image of linear operators and the sum of closed vector subspaces of a Banach space.

  9. Commutators Generated by Singular Integral Operators with Variable Kernels and Local Campanato Functions on Generalized Local Morrey Spaces

    Mo, Huixia; Xue, Hongyang
    In this paper, we obtain the boundedness for the singular integral operator with rough variable kernel $T_\Omega$ on the generalized local Morrey spaces, as well as the boundedness for the multilinear commutators generated by $T_\Omega$ and local Campanato functions.

  10. A Class of Parabolic Maximal Functions

    Shakkah, Ghada; Al-Salman, Ahmad
    In this paper, we prove $L^{p}$ estimates of a class of parabolic maximal functions provided that their kernels are in $L^{q}$. Using the obtained estimates, we prove the boundedness of the maximal functions under very weak conditions on the kernel. In particular, we prove the$\ L^{p}$-boundedness of our maximal functions when their kernels are in $L\log L^{\frac{1}{2}}(\mathbb{S}^{n-1})$ or in the block space $B_{q}^{0,-1/2}(\mathbb{S}^{n-1}),$ $q>1$.

  11. Wave Operators and Similarity for Long Range $N$-body Schrödinger Operators

    Kitada, Hitoshi
    We consider asymptotic behavior of $e^{-itH}f$ for $N$-body Schrödigner operator $H=H_{0}+\sum_{1 \leq i < j \leq N } V_{ij}(x)$ with long- and short-range pair potentials $V_{ij}(x)=V_{ij}^L(x)+V_{ij}^S(x)$ $(x\in {\mathbb R}^\nu)$ such that $\partial_x^\alpha V_{ij}^L(x)=O(|x|^{-\delta |\alpha|})$ and $V_{ij}^S(x)=O(|x|^{-1-\delta})$ $(|x|\to\infty)$ with $\delta>0$. Introducing the concept of scattering spaces which classify the initial states $f$ according to the asymptotic behavior of the evolution $e^{-itH}f$, we give a generalized decomposition theorem of the continuous spectral subspace ${\mathcal H}_c(H)$ of $H$. The asymptotic completeness of wave operators is proved for some long-range pair potentials with $\delta>1/2$ by using this decomposition theorem under some assumption on subsystem eigenfunctions.

  12. Special Issue of Communications in Mathematical Analysis Dedicated to Tosio Kato

    Diagana, Toka
    This Interview is a part of the Special Issue of Communications in Mathematical Analysis dedicated to late Prof. Tosio Kato on his 100th birthday. We extend our deepest thanks to Prof. Hitoshi Kitada for dedicating his paper "Wave Operators and Similarity for Long Range N-body Schrodinger Operators" to Prof. Tosio Kato. Further, we thank him for accepting to answer to our questions.

  13. Fixed Point Theorems for Positive Maps and Applications

    Benmezai, Abdelhamid; Mechrouk, Salima; Henderson, Johnny
    We prove in this article new fixed point theorems for positive maps having approximative minorant and majorant at $0$ and $\infty$ in specific classes of operators. Then, the new fixed point theorems are used to obtain existence results for positive solutions to boundary value problems involving a generalized $p(t)$-Laplacian operator.

  14. The Egoroff Theorem for Operator-Valued Measures in Locally Convex Spaces

    Haluska, Jan; Hutnik, Ondrej
    The Egoroff theorem for measurable ${\mathbb X}$-valued functions and operator-valued measures ${\mathbb m}: \Sigma \to L({\mathbb X}, {\mathbb Y})$ is proved, where $\Sigma$ is a $\sigma$-algebra of subsets of $T \neq \emptyset$ and ${\mathbb X}$, ${\mathbb Y}$ are both locally convex spaces.

  15. Extremal Viscosity Solutions of Almost Periodic Hamilton-Jacobi Equations

    Belloni, Marino; Marchi, Silvana
    This paper deals with viscosity solutions of Hamilton-Jacobi equations in which the Hamiltonian $H$ is weakly monotone with respect to the zero order term: this leads to non-uniqueness of solutions, even in the class of periodic or almost periodic (briefly a.p.) functions. The lack of uniqueness of a.p. solutions leads to introduce the notion of minimal (maximal) a.p. solution and to study its properties. The classes of asymptotically almost periodic (briefly a.a.p.) and pseudo almost periodic (briefly p.a.p.) functions are also considered.

  16. On the Maximality of Certain Hyperellptic Curves with an Application to Character Sums Peter McCalla and Francois Ramaroson

    McCalla, Peter; Ramaroson, Francois
    In [4], Kodama, Top, Washio studied the maximality of a family of elliptic curves, mostly of genus 3, over a finite field. They used the Jacobians of the curves and differential forms to obtain their results. In this note, in order to prove the maximality of the curves under study, we use analytical tools, namely character and Jacobsthal sums, together with an important result which says that if a curve is the image of a maximal curve under a rational map, then it is itself maximal. Character sums are suitable for counting the number of points on a curve over a finite field, and their use makes...

  17. New Developments on Nirenberg's Problem for Compact Perturbations of Quasimonotone Expansive Mappings in Reflexive Banach Spaces

    Asfaw, Teffera M.
    Let $X$ be a real locally uniformly convex reflexive Banach space with locally uniformly convex dual space $X^*$. Let $T:X\to X^*$ be demicontinuous, quasimonotone and $\alpha$-expansive, and $C: X\to X^*$ be compact such that either (i) $\langle Tx+Cx, x\rangle \geq -d\|x\|$ for all $x\in X$ or (ii) $\langle Tx+Cx, x\rangle \geq-d\|x\|^2$ for all $x\in X$ and some suitable positive constants $\alpha$ and $d.$ New surjectivity results are given for the operator $T+C.$ The results are new even for $C=\{0\}$, which gives a partial positive answer for Nirenberg's problem for demicontinuous, quasimonotone and $\alpha$-expansive mapping. Existence result on the surjectivity of quasimonotone perturbations of multivalued maximal monotone operator is included. The...

  18. A Note on the Inhomogeneous Schrödinger Equation with Mixed Power Nonlinearity

    Hezzi, H.; Marzouk, A.; Saanouni, T.
    We investigate the initial value problem for an inhomogeneous nonlinear Schrödinger equation with a combined power nonlinearity. We prove global well-posedness in the defocusing case. In the focusing case, we prove existence of ground state and nonlinear instability of standing waves.

  19. Degenerate Abstract Parabolic Equations and Applications

    Shakhmurov, Veli.B.; Sahmurova, Aida
    Linear and nonlinear degenerate abstract parabolic equations with variable coefficients are studied. Here the equations and boundary conditions are degenerated on all boundary and contain some parameters. The linear problem is considered on the moving domain. The separability properties of elliptic and parabolic problems and Strichartz type estimates in mixed $L_{\mathbf{p}} $ spaces are obtained. Moreover, the existence and uniqueness of optimal regular solution of mixed problem for nonlinear parabolic equation is established. Note that, these problems arise in fluid mechanics and environmental engineering.

  20. Anisotropic Herz Spaces with Variable Exponents

    Wang, Hongbin
    In this paper, we introduce the anisotropic Herz spaces with two variable exponents and establish their block decomposition. Using this decomposition, we obtain some boundedness on the anisotropic Herz spaces with two variable exponents for a class of sublinear operators.

Aviso de cookies: Usamos cookies propias y de terceros para mejorar nuestros servicios, para análisis estadístico y para mostrarle publicidad. Si continua navegando consideramos que acepta su uso en los términos establecidos en la Política de cookies.