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By
Almahalebi, Muaadh; Chahbi, Abdellatif
The aim of this paper is to introduce and solve the
pradical functional equation
$$f\left( {\sqrt[p]{{x^p + y^p }}} \right) = f\left( x \right) + f\left( y \right),p \in \mathbb{N}_2 .$$
We also state an analogue of the fixed point theorem [12, Theorem 1] in 2Banach spaces and investigate stability for this equation in 2Banach spaces.
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By
Ji, Lina; Zheng, Xiangqi
For continuousstate branching processes in Lévy random environments, the recursion of nmoments and the equivalent condition for the existence of general fmoments are established, where f is a positive continuous function satisfying some standard conditions.
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By
Liang, Zaitao; Yang, Yanjuan
In this paper, we study the existence of nontrivial radial convex solutions of a singular Dirichlet problem involving the mean curvature operator in Minkowski space. The proof is based on a wellknown fixed point theorem in cones. We deal with more general nonlinear term than those in the literature.
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By
Hu, Zejun; Yin, Jiabin
Associated with an immersion φ : S^{3} → ℂP^{3}, we can define a canonical bundle endomorphism F : TS^{3} → TS^{3} by the pull back of the Kahler form of ℂP^{3}. In this article, related to F we study equivariant minimal immersions from S^{3} into ℂP^{3} under the additional condition (∇_{X}F)X = 0 for all X ∈ ker (F). As main result, we give a complete classification of such kinds of immersions. Moreover, we also construct a typical example of equivariant nonminimal immersion φ: S^{3} → ℂP^{3} satisfying (∇_{X}F)X = 0 for all X ∈ ker (F), which is neither Lagrangian nor of CR type.
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By
Balan, Raluca M; QuerSardanyons, Lluís; Song, Jian
In this article, we consider the Parabolic Anderson Model with constant initial condition, driven by a spacetime homogeneous Gaussian noise, with general covariance function in time and spatial spectral measure satisfying Dalang’s condition. First, we prove that the solution (in the Skorohod sense) exists and is continuous in L^{p} (Ω). Then, we show that the solution has a modification whose sample paths are Hölder continuous in space and time, under the minimal condition on the spatial spectral measure of the noise (which is the same as the condition encountered in the case of the white noise in time). This improves similar results which were obtained in [6, 10] under more restrictive conditions, and with suboptimal exponents for Hölder continuity.
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By
Dai, Shaoyu; Chen, Huaihui
We establish a precise Schwarz lemma for realvalued and bounded harmonic functions in the real unit ball of dimension n. This extends Chen’s SchwarzPick lemma for realvalued and bounded planar harmonic mapping.
By
Peng, Ru; Xing, Xiaolei; Jiang, Liangying
This article is devoted to characterizing the boundedness and compactness of multiplication operators from Hardy spaces to weighted Bergman spaces in the unit ball of ℂ^{n}.
By
Yang, Xianyong; Zhang, Wei; Zhao, Fukun
In this article, we are concerned with the existence of solutions of a quasilinear elliptic equation in ℝ^{N} which includes the socalled modified nonlinear Schrödinger equation as a special case. Combining the dual approach and the nonsmooth critical point theory, we obtain the existence of a nontrivial solution.
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By
Chen, Hua; Xu, Huiyang
In this paper, we study the initialboundary value problem for the semilinear parabolic equations u_{t} − ∆_{X}u = u^{p−1}u, where X = (X_{1}, X_{2}, ⋯ , X_{m}) is a system of real smooth vector fields which satisfy the Hörmander’s condition, and
$$\Delta_X\;=\;\sum\limits_{j = 1}^m\;{X_j^2}$$
finitely degenerate elliptic operator. Using potential well method, we first prove the invariance of some sets and vacuum isolating of solutions. Finally, by the Galerkin method and the concavity method we show the global existence and blowup in finite time of solutions with low initial energy or critical initial energy, and also we discuss the asymptotic behavior of the global solutions.
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By
Zhang, Yingshu; Li, Lang; Fang, Shaomei
The Cauchy problem of the generalized KuramotoSivashinsky equation in multidimensions (n ≥ 3) is considered. Based on Green’s function method, some ingenious energy estimates are given. Then the global existence and pointwise convergence rates of the classical solutions are established. Furthermore, the L^{p} convergence rate of the solution is obtained.
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