Infinitely many solutions for a resonant sublinear Schrödinger equation

In this paper, we consider a nonlinear sublinear Schrödinger equation at resonance in . By using bounded domain approximation technique, we prove that the problem has infinitely many solutions. Copyright © 2013 John Wiley & Sons, Ltd.     

Classification of Nonoscillatory Solutions of a Higher Order Neutral Difference Equation

In this paper, classification schemes are given for the nonoscillatory solutions of higher order neutral difference equations. Several necessary and/or sufficient conditions are obtained for the existence of each kind of solution.     

On the Inner and Outer Norms of Sublinear Mappings

In this short note we show that the outer norm of a sublinear mapping F, acting between Banach spaces X and Y and with dom F = X, is finite only if F is single-valued. This implies in particular that for a sublinear multivalued mapping the inner and the outer norms cannot be finite simultaneously.      

Optimality Conditions and Duality in Nondifferentiable Minimax Fractional Programming with Generalized Convexity

We establish sufficient optimality conditions for a class of nondifferentiable minimax fractional programming problems involving (F, α, ρ, d)-convexity. Subsequently, we apply the optimality conditions to formulate two types of dual problems and prove appropriate duality theorems. The authors thank the referee for valuable suggestions improving the presentation of the paper.     

Another characterization of the Hardy space with non doubling measures

Let μ be a Radon measure on ?^d which may be non doubling, and let H ¹(μ) be the Hardy space associated with μ introduced by Tolsa. In this paper, a new atomic characterization of H ¹(μ) is established. Some applications of this characterization are also given. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Riesz potential operator in continual variable exponents Herz spaces

We find conditions on the variable parameters $p\left(x\right),q\left(t\right)$ and $\alpha \left(t\right)$, defining the Herz space $H^{p(·),q(·),\alpha (·)}\left({\mathbb{R}}^n\right)$, for the validity of Sobolev type theorem for the Riesz potential operator to be bounded within the frameworks of such variable exponents Herz spaces. We deal with a “continual” version of Herz spaces (which coincides with the “discrete” one when q is constant).     

非线性二阶微分方程的振动准则

本文建立了非线性二阶微分方程(a(t)x′(t))′+p(t)x′(t)+q(t)|x(t)|^α sgn x(t)=0的一个新的振动准则，并改进了文［１］的结果。     

Finding cycles and trees in sublinear time

We present sublinear‐time (randomized) algorithms for finding simple cycles of length at least and tree‐minors in bounded‐degree graphs. The complexity of these algorithms is related to the distance of the graph from being C_k‐minor free (resp., free from having the corresponding tree‐minor). In particular, if the graph is ‐far from being cycle‐free (i.e., a constant fraction of the edges must be deleted to make the graph cycle‐free), then the algorithm finds a cycle of polylogarithmic length in time , where N denotes the number of vertices. This time complexity is optimal up to polylogarithmic factors. The foregoing results are the outcome of our study of the complexity of one‐sided error property testing algorithms in the bounded‐degree graphs model. For example, we show that cycle‐freeness of N‐vertex graphs can be tested with one‐sided error within time complexity , where ? denotes the proximity parameter. This matches the known query lower bound for one‐sided error cycle‐freeness testing, and contrasts with the fact that any minor‐free property admits a two‐sided error tester of query complexity that only depends on ?. We show that the same upper bound holds for testing whether the input graph has a simple cycle of length at least k, for any . On the other hand, for any fixed tree T, we show that T‐minor freeness has a one‐sided error tester of query complexity that only depends on the proximity parameter ?. Our algorithm for finding cycles in bounded‐degree graphs extends to general graphs, where distances are measured with respect to the actual number of edges. Such an extension is not possible with respect to finding tree‐minors in complexity. © 2012 Wiley Periodicals, Inc. Random Struct. Alg., 45, 139–184, 2014     

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Strong laws of large numbers play key role in nonadditive probability theory. Recently, there are many research papers about strong laws of large numbers for independently and identically distributed (or negatively dependent) random variables in the framework of nonadditive probabilities (or nonlinear expectations). This paper introduces a concept of weakly negatively dependent random variables and investigates the properties of such kind of random variables under a framework of nonadditive probabilities and sublinear expectations. A strong law of large numbers is also proved for weakly negatively dependent random variables under a kind of sublinear expectation as an application