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1.
Tarek F. Ibrahim Nouressadat Touafek 《Mathematical Methods in the Applied Sciences》2014,37(16):2562-2569
This paper deals with the form and the periodicity of the solutions of the max‐type system of difference equations where , and are positive two‐periodic sequences and initial values x0, x ? 1, y0, y ? 1 ∈ (0, + ∞ ). Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
2.
We study the problem of identifying unknown source terms in an inverse parabolic problem, when the overspecified (measured) data are given in form of Dirichlet boundary condition u(0,t) = h(t) and , where is an arbitrarily prescribed subregion. The main goal here is to show that the gradient of cost functional can be expressed via the solutions of the direct and corresponding adjoint problems. We prove Hölder continuity of the cost functional and derive the Lipschitz constant in the explicit form via the given data. On the basis of the obtained results, we propose a monotone iteration process. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
3.
Real‐variable characterizations of Musielak–Orlicz–Hardy spaces associated with Schrödinger operators on domains
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Der‐Chen Chang Zunwei Fu Dachun Yang Sibei Yang 《Mathematical Methods in the Applied Sciences》2016,39(3):533-569
Let n≥3, Ω be a strongly Lipschitz domain of and LΩ:=?Δ+V a Schrödinger operator on L2(Ω) with the Dirichlet boundary condition, where Δ is the Laplace operator and the nonnegative potential V belongs to the reverse Hölder class for some q0>n/2. Assume that the growth function satisfies that ?(x,·) is an Orlicz function, (the class of uniformly Muckenhoupt weights) and its uniformly critical lower type index , where and μ0∈(0,1] denotes the critical regularity index of the heat kernels of the Laplace operator Δ on Ω. In this article, the authors first show that the heat kernels of LΩ satisfy the Gaussian upper bound estimates and the Hölder continuity. The authors then introduce the ‘geometrical’ Musielak–Orlicz–Hardy space via , the Hardy space associated with on , and establish its several equivalent characterizations, respectively, in terms of the non‐tangential or the vertical maximal functions or the Lusin area functions associated with LΩ. All the results essentially improve the known results even on Hardy spaces with p∈(n/(n + δ),1] (in this case, ?(x,t):=tp for all x∈Ω and t∈[0,∞)). Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
4.
In this paper, we study the following modified Kirchhoff‐type equations of the form: where a > 0, b ≥ 0, and . Under appropriate assumptions on V (x) and h(x,u), some existence results for positive solutions, negative solutions, and sequence of high energy solutions are obtained via a perturbation method. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
5.
Sadek Gala Yoshihiro Sawano Hitoshi Tanaka 《Mathematical Methods in the Applied Sciences》2012,35(11):1321-1334
In this work, we are interested in the study of regularity for the three‐dimensional magneto‐micropolar fluid equations in Orlicz–Morrey spaces. If the velocity field satisfies or the gradient field of velocity satisfies then we show that the solution remains smooth on [0,T]. In view of the embedding with 2 < p < 3 ∕ r and P > 1, we see that our result extends the result of Yuan and that of Gala. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
6.
《Mathematical Methods in the Applied Sciences》2018,41(13):5050-5064
In this paper, we consider the following fractional Schrödinger‐Poisson system where 0 < t ≤ α < 1, , and 4α+2t ≥3 and the functions V(x), K(x) and f(x) have finite limits as |x|→∞. By imposing some suitable conditions on the decay rate of the functions, we prove that the above system has two nontrivial solutions. One of them is positive and the other one is sign‐changing. Recent results from the literature are generally improved and extended. 相似文献
7.
In this paper, by an approximating argument, we obtain infinitely many solutions for the following Hardy–Sobolev equation with critical growth: provided N > 6 + t, where and Ω is an open bounded domain in , which contains some points x0 = (0,z0). Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
8.
Liang Zhao 《Mathematical Methods in the Applied Sciences》2014,37(5):744-751
In this paper, we show the following main results. Let (Mn,g(t)), t ∈ [0,T), be a solution of the unnormalized Hk ? flow on a closed manifold, and λ1,p(t) be the first eigenvalue of the p‐Laplace operator. If there exists a nonnegative constant ε such that in M × [0,T) and in M × [0,T),then λ1,p(t) is increasing and the differentiable almost everywhere along the unnormalized Hk ? flow on [0,T). At last, we discuss some useful monotonic quantities. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
9.
Boundedness of solutions to parabolic–elliptic Keller–Segel systems with signal‐dependent sensitivity
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Kentarou Fujie Michael Winkler Tomomi Yokota 《Mathematical Methods in the Applied Sciences》2015,38(6):1212-1224
This paper deals with the parabolic–elliptic Keller–Segel system with signal‐dependent chemotactic sensitivity function, under homogeneous Neumann boundary conditions in a smooth bounded domain , with initial data satisfying u0 ≥ 0 and . The chemotactic sensitivity function χ(v) is assumed to satisfy The global existence of weak solutions in the special case is shown by Biler (Adv. Math. Sci. Appl. 1999; 9:347–359). Uniform boundedness and blow‐up of radial solutions are studied by Nagai and Senba (Adv. Math. Sci. Appl. 1998; 8:145–156). However, the global existence and uniform boundedness of classical nonradial solutions are left as an open problem. This paper gives an answer to the problem. Namely, it is shown that the system possesses a unique global classical solution that is uniformly bounded if , where γ > 0 is a constant depending on Ω and u0. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
10.
Reza Mazrooei‐Sebdani 《Mathematical Methods in the Applied Sciences》2014,37(4):518-523
Consider the non‐autonomous equations: where and also These are some non‐autonomous homogeneous rational difference equations of degree one. A reduction in order is consi‐dered. Convergence and monoton character of positive solutions are studied. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
11.
Qiaoshun Yang Baoguo Jia Zhiting Xu 《Mathematical Methods in the Applied Sciences》2016,39(2):202-213
In this paper, we consider the nonlinear oscillation of the following second‐order neutral delay dynamic equations with distributed delay on a time scale , where Z(t) = x(t) + p(t)x(τ(t)),α,β > 0 are constants. By using some new techniques, we obtain oscillation criteria for the equation when β > α,β = α, and β < α, respectively. Those results established here complete and develop the oscillation criteria in the literature. Also, our main results are illustrated with some examples. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
12.
We study the large time behavior of non‐negative solutions to the nonlinear fractional reaction–diffusion equation ?tu = ? tσ( ? Δ)α ∕ 2u ? h(t)up (α ∈ (0,2]) posed on and supplemented with an integrable initial condition, where σ ≥ 0, p > 1, and h : [0, ∞ ) → [0, ∞ ). Defining the mass , under certain conditions on the function h, we show that the asymptotic behavior of the mass can be classified along two cases as follows:
- if , then there exists M ∞ ∈ (0, ∞ ) such that ;
- if , then .
13.
Patrizio Neff Dirk Pauly Karl‐Josef Witsch 《Mathematical Methods in the Applied Sciences》2012,35(1):65-71
For a bounded domain with connected Lipschitz boundary, we prove the existence of some c > 0, such that holds for all square‐integrable tensor fields , having square‐integrable generalized “rotation” tensor fields and vanishing tangential trace on ?Ω, where both operations are to be understood row‐wise. Here, in each row, the operator curl is the vector analytical reincarnation of the exterior derivative d in . For compatible tensor fields T, that is, T = ? v, the latter estimate reduces to a non‐standard variant of Korn's first inequality in , namely for all vector fields , for which ? vn,n = 1, … ,N, are normal at ?Ω. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
14.
In this paper, we consider the multiplicity results of nontrivial nonnegative solutions of the quasilinear p‐Laplacian system with the nonlinear boundary conditions: (0.1) where Ω is a smooth exterior domain in is the outward normal derivative on the boundary Γ = ?Ω, and . By the Nehari manifold and variational methods, we prove that the problem (0.1) has at least two nontrivial nonnegative solutions when the pair of the parameters (λ,μ) belongs to a certain subset of . Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
15.
Aldo T. Lourêdo M.A. Ferreira de Araújo M. Milla Miranda 《Mathematical Methods in the Applied Sciences》2014,37(9):1278-1302
This paper is concerned with the existence and decay of solutions of the mixed problem for the nonlinear wave equation with boundary conditions Here, Ω is an open bounded set of with boundary Γ of class C2; Γ is constituted of two disjoint closed parts Γ0 and Γ1 both with positive measure; the functions μ(t), f(s), g(s) satisfy the conditions μ(t) ≥ μ0 > 0, f(s) ≥ 0, g(s) ≥ 0 for t ≥ 0, s ≥ 0 and h(x,s) is a real function where x ∈ Γ1, ν(x) is the unit outward normal vector at x ∈ Γ1 and α, β are non‐negative real constants. Assuming that h(x,s) is strongly monotone in s for each x ∈ Γ1, it is proved the global existence of solutions for the previous mixed problem. For that, it is used in the Galerkin method with a special basis, the compactness approach, the Strauss approximation for real functions and the trace theorem for nonsmooth functions. The exponential decay of the energy is derived by two methods: by using a Lyapunov functional and by Nakao's method. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
16.
Houyu Zhao 《Mathematical Methods in the Applied Sciences》2014,37(17):2689-2696
In this paper, we study the existence of analytic invariant curves of a iterative equation which from mosquito model. By constructing an invertible analytic solution g(x) of an auxiliary equation of the form invertible analytic solutions of the form g(αg ? 1(x)) for the original iterative functional equation are obtained. Besides the hyperbolic case 0 < | α | < 1, we focus on those α on the unit circle S1, that is, | α | = 1. We discuss not only those α at resonance, that is at a root of the unity, but also those α near resonance under the Brjuno condition. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
17.
A complete upper estimate on the localization for the degenerate parabolic equation with nonlinear source
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This paper deals with the Cauchy problem for the degenerate parabolic equation with a strongly nonlinear source where N ≥ 1, p > 2, q ≥ p ? 1, and the blow‐up time T < ∞ . It has been shown that the solution u(x,t) is strictly localized for q ≥ p ? 1, provided that the initial function u0(x) has a compact support by Liang and Zhao. In addition, if q > 2p ? 1, an upper estimate on the localization in terms of the initial support and the blow‐up time T is partially derived by Liang. In this work, by using the De Giorgi‐type iteration technique, we give a complete estimate on the localization for all q ≥ p ? 1. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
18.
Ground state solutions for asymptotically periodic fractional Schrödinger–Poisson problems with asymptotically cubic or super‐cubic nonlinearities
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Sitong Chen Jiawu Peng Xianhua Tang 《Mathematical Methods in the Applied Sciences》2017,40(13):4948-4961
In this paper, we consider the following fractional Schrödinger–Poisson problem: where s,t∈(0,1],4s+2t>3,V(x),K(x), and f(x,u) are periodic or asymptotically periodic in x. We use the non‐Nehari manifold approach to establish the existence of the Nehari‐type ground state solutions in two cases: the periodic one and the asymptotically periodic case, by introducing weaker conditions uniformly in with and with constant θ0∈(0,1), instead of uniformly in and the usual Nehari‐type monotonic condition on f(x,τ)/|τ|3. Our results unify both asymptotically cubic or super‐cubic nonlinearities, which are new even for s=t=1. Copyright © 2017 John Wiley & Sons, Ltd. 相似文献
19.
In this paper, we are concerned with the existence of positive solutions for the following nonlocal BVP of fractional DEs with p‐Laplacian operator By using the fixed point theorem in a cone, multiplicity solutions of the BVP are obtained. An example is also given to show the effectiveness of the obtained result. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
20.
On the ‐boundedness of solution operator families of the generalized Stokes resolvent problem in an infinite layer
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Hirokazu Saito 《Mathematical Methods in the Applied Sciences》2015,38(9):1888-1925
In this paper, we prove the ‐boundedness of solution operator families of the generalized Stokes resolvent problem in an infinite layer with resolvent parameter , where , and our boundary conditions are nonhomogeneous Neumann on upper boundary and Dirichlet on lower boundary. We want to emphasize that we can choose 0 < ? < π ∕ 2 and γ0 > 0 arbitrarily, although usual parabolic theorem tells us that we must choose a large γ0 > 0 for given 0 < ? < π ∕ 2. We also prove the maximal Lp ? Lq regularity theorem of the nonstationary Stokes problem as an application of the ‐boundedness. The key of our approach is to apply several technical lemmas to the exact solution formulas of a resolvent problem. The formulas are obtained through the solutions of the ODEs, in the Fourier space, driven by the partial Fourier transform with respect to tangential space variable . Copyright © 2014 John Wiley & Sons, Ltd. 相似文献