## Recursos de colección

#### Project Euclid (Hosted at Cornell University Library) (204.172 recursos)

Taiwanese Journal of Mathematics

1. #### Existence of Weak Solution for a Class of Abstract Coupling System Associated with Stationary Electromagnetic System

Aramaki, Junichi
We consider the existence of a weak solution for a class of coupling system containing stationary electromagnetic coupling system associated with the Maxwell equations in a multi-connected domain. Mathematically we are concerned with the coupled system containing a $p$-curl equation and a $q$-Laplacian equation.

2. #### An Existence Result for Discrete Anisotropic Equations

Heidarkhani, Shapour; Afrouzi, Ghasem A.; Moradi, Shahin
A critical point result is exploited in order to prove that a class of discrete anisotropic boundary value problems possesses at least one solution under an asymptotical behaviour of the potential of the nonlinear term at zero. Some recent results are extended and improved. Some examples are presented to demonstrate the applications of our main results.

3. #### Global Existence of Weak Solutions for the Nonlocal Energy-weighted Reaction-diffusion Equations

Chang, Mao-Sheng; Wu, Hsi-Chun
The reaction-diffusion equations provide a predictable mechanism for pattern formation. These equations have a limited applicability. Refining the reaction-diffusion equations must be a good way for supplying the gap between the mathematical simplicity of the model and the complexity of the real world. In this manuscript, we introduce a modified version of reaction-diffusion equation, which we have named ‘‘nonlocal energy-weighted reaction-diffusion equation’’. For any bounded smooth domain $\Omega \subset \mathbb{R}^n$, we establish the global existence of weak solutions $u \in L^2(0,T;H^1_0(\Omega))$ with $u_t \in L^2(0,T;H^{-1}(\Omega))$ to the initial boundary value problem of the nonlocal energy-weighted reaction-diffusion equation for any initial...

4. #### Multiplication of Distributions and Travelling Wave Solutions for the Keyfitz-Kranzer System

Sarrico, Carlos Orlando R.
The present paper concerns the study of distributional travelling waves for the model problem $u_{t} + (u^{2}-v)_{x} = 0$, $v_{t} + (u^{3}/3-u)_{x} = 0$, also called the Keyfitz-Kranzer system. In the setting of a product of distributions, which is not defined by approximation processes, we are able to define a rigourous concept of a solution which extends the classical solution concept. As a consequence, we will establish necessary and sufficient conditions for the propagation of distributional profiles and explicit examples are given. A survey of the main ideas and formulas for multiplying distributions is also provided.

5. #### Liouville Type Theorems for General Integral System with Negative Exponents

Liu, Zhao; Chen, Lu; Wang, Xumin
In this paper, we establish a Liouville type theorem for the following integral system with negative exponents $\begin{cases} u(x) = \int_{\mathbb{R}^n} |x-y|^{\nu} f(u,v)(y) \, dy, & x \in \mathbb{R}^n, \\ v(x) = \int_{\mathbb{R}^n} |x-y|^{\nu} g(u,v)(y) \, dy, & x \in \mathbb{R}^n, \end{cases}$ where $n \geq 1$, $\nu \gt 0$, and $f$, $g$ are continuous functions defined on $\mathbb{R}_{+} \times \mathbb{R}_{+}$. Under nature structure conditions on $f$ and $g$, we classify each pair of positive solutions for above integral system by using the method of moving sphere in integral forms. Moreover, some other Liouville theorems are established for similar...

6. #### Existence and Multiplicity of Solutions for a Quasilinear Elliptic Inclusion with a Nonsmooth Potential

Yuan, Ziqing; Huang, Lihong; Wang, Dongshu
This paper is concerned with a nonlinear elliptic inclusion driven by a multivalued subdifferential of nonsmooth potential and a nonlinear inhomogeneous differential operator. We obtain two multiplicity theorems in the Orlicz-Sobolev space. In the first multiplicity theorem, we produce three nontrivial smooth solutions. Two of these solutions have constant sign (one is positive, the other is negative). In the second multiplicity theorem, we derive an unbounded sequence of critical points for the problem. Our approach is variational, based on the nonsmooth critical point theory. We also show that $C^1$-local minimizers are also local minimizers in the Orlicz-Sobolev space for a...

7. #### Positive Approximation Properties of Banach Lattices

Chen, Dongyang
In this paper, an equivalent formulation of extendable local reflexivity (ELR) introduced by Oikhberg and Rosenthal is given. We introduced the positive version (PELR) of the ELR in Banach lattices to solve the lifting problem for the bounded positive approximation property (BPAP). It is proved that a Banach lattice $X$ has the BPAP and is PELR if and only if the dual space $X^{*}$ of $X$ has the BPAP. Finally, we give isometric factorizations of positive weakly compact operators and establish some new characterizations of positive approximation properties.

8. #### Erratum to: Two Optimal Inequalities for Anti-holomorphic Submanifolds and Their Applications

Al-Solamy, Falleh R.; Chen, Bang-Yen; Deshmukh, Sharief
Theorem 4.1 of [1] is not correctly stated. In this erratum we make a correction on Theorem 4.1. As a consequence, we also make the corresponding correction on Theorem 5.2 of [1].

9. #### Algebraic Surfaces with Zero-dimensional Cohomology Support Locus

Wang, Botong
Using the theory of cohomology support locus, we give a necessary condition for the Albanese map of a smooth projective surface to be a submersion. More precisely, assuming that the cohomology support locus of any finite abelian cover of a smooth projective surface consists of finitely many points, we prove that the surface has trivial first Betti number, or is a ruled surface of genus one, or is an abelian surface.

10. #### Minimal Ruled Submanifolds Associated with Gauss Map

Jung, Sun Mi; Kim, Dong-Soo; Kim, Young Ho
We set up the new models of product manifolds, namely a generalized circular cylinder and a generalized hyperbolic cylinder as cylindrical types of ruled submanifold in Minkowski space. We also establish some characterizations of generalized circular cylinders and hyperbolic cylinders in Minkowski space with the Gauss map. We also show that there do not exist non-cylindrical marginally trapped ruled submanifolds with the pointwise $1$-type Gauss map of the first kind, which gives a characterization of non-cylindrical minimal ruled submanifolds in Minkowski space.

11. #### Primitive Submodules, Co-semisimple and Regular Modules

Medina-Bárcenas, Mauricio; Özcan, A. Çiğdem
In this paper, primitive submodules are defined and various properties of them are investigated. Some characterizations of co-semisimple modules are given and several conditions under which co-semisimple and regular modules coincide are discussed.

12. #### Stuffle Product Formulas of Multiple Zeta Values

Li, Zhonghua; Qin, Chen
Using the combinatorial descriptions of stuffle product, we obtain recursive formulas for the stuffle product of multiple zeta values and of multiple zeta-star values. Then we apply the formulas to prove several stuffle product formulas with one or two strings of $z_p$'s. We also describe how to use our formulas in general cases.

13. #### Distance Eigenvalues and Forwarding Indices of Circulants

Liu, Shuting; Lin, Huiqiu; Shu, Jinlong
In this paper, we give the distance spectral radii of several classes of circulant graphs. We also list the elements in the first rows of their corresponding distance matrices, with which all other distance eigenvalues can be obtained. In addition, we get the relationships between the distance spectral radii and forwarding indices of circulant graphs. Finally, the exact values of the vertex-forwarding indices and some bounds of the edge-forwarding indices for these kinds of graphs are presented.

14. #### Coderivatives Related to Parametric Extended Trust Region Subproblem and Their Applications

Tran, Van Nghi
This paper deals with the Fréchet and Mordukhovich coderivatives of the normal cone mapping related to the parametric extended trust region subproblems (eTRS), in which the trust region intersects a ball with a single linear inequality constraint. We use the obtained results to investigate the Lipschitzian stability of parametric eTRS. We also propose a necessary condition for the local (or global) solution of the eTRS by using the coderivative tool.

15. #### The Spectral Method for Long-time Behavior of a Fractional Power Dissipative System

Lu, Hong; Zhang, Mingji
In this paper, we consider the fractional complex Ginzburg-Landau equation in two spatial dimensions with the dissipative effect given by a fractional Laplacian. The periodic initial value problem of the fractional complex Ginzburg-Landau equation is discretized fully by Galerkin-Fourier spectral method, and the dynamical behaviors of the discrete system are studied. The existence and convergence of global attractors of the discrete system are obtained by a priori estimates and error estimates of the discrete solution. The numerical stability and convergence of the discrete scheme are proved.

16. #### Periodic Solutions of Sublinear Impulsive Differential Equations

Niu, Yanmin; Li, Xiong
In this paper, we consider sublinear second order differential equations with impulsive effects. Basing on the Poincaré-Bohl fixed point theorem, we first will prove the existence of harmonic solutions. The existence of subharmonic solutions is also obtained by a new twist fixed point theorem recently established by Qian etc in 2015 [18].

17. #### Fixed Point Theorems via MNC in Ordered Banach Space with Application to Fractional Integro-differential Evolution Equations

Nashine, Hemant Kumar; Yang, He; Agarwal, Ravi P.
In this paper, we propose fixed point results through the notion of measure of noncompactness (MNC) in partially ordered Banach spaces. We also prove some new coupled fixed point results via MNC for more general class of function. To achieve this result, we relaxed the conditions of boundedness, closedness and convexity of the set at the expense that the operator is monotone and bounded. Further, we apply the obtained fixed point theorems to prove the existence of mild solutions for fractional integro-differential evolution equations with nonlocal conditions. At the end, an example is given to illustrate the rationality of the...

18. #### Existence of Solutions to Quasilinear Schrödinger Equations Involving Critical Sobolev Exponent

Wang, Youjun; Li, Zhouxin
By using variational approaches, we study a class of quasilinear Schrödinger equations involving critical Sobolev exponents $-\Delta u + V(x)u + \frac{1}{2} \kappa [\Delta(u^2)]u = |u|^{p-2}u + |u|^{2^*-2}u, \quad x \in \mathbb{R}^N,$ where $V(x)$ is the potential function, $\kappa \gt 0$, $\max \{ (N+3)/(N-2),2 \} \lt p \lt 2^* := 2N/(N-2)$, $N \geq 4$. If $\kappa \in [0,\overline{\kappa})$ for some $\overline{\kappa} \gt 0$, we prove the existence of a positive solution $u(x)$ satisfying $\max_{x \in \mathbb{R}^N} |u(x)| \leq \sqrt{1/(2\kappa)}$.

19. #### Toeplitz Operator for Dirichlet Space Through Sobolev Multiplier Algebra

Luo, Shuaibing; Xiao, Jie
This paper is mainly concerned with the Toeplitz operator $T_{\phi}$ over the Dirichlet space $\mathcal{D}$ with the symbol $\phi$ in the Sobolev multiplier algebra $M(W^{1,2}(\mathbb{D}))$, thereby extending several known ones in a very different manner.

20. #### Exact Controllability for Wave Equations with Switching Controls

He, Yong
In this paper, we analyze the exact controllability problem for wave equations endowed with switching controls. The goal is to control the dynamics of the system by switching among different actuators such that, in each instant of time, there are as few active actuators as possible. We prove that the system is exactly controllable under suitable geometric control conditions.

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