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991.
Existence of multiplicity harmonic and subharmonic solutions for second‐order quasilinear equation via Poincaré‐Birkhoff twist theorem
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In this paper, we investigate the existence and multiplicity of harmonic and subharmonic solutions for second‐order quasilinear equation where , g satisfies the superlinear condition at infinity. We prove that the given equation possesses harmonic and subharmonic solutions by using the phase‐plane analysis methods and a generalized version of the Poincaré‐Birkhoff twist theorem. 相似文献
992.
Integral representation and estimation of harmonic functions in the quaternionic half space
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《Mathematical Methods in the Applied Sciences》2017,40(15):5484-5489
In this article, we discuss the integral representation of quaternionic harmonic functions in the half space with the general boundary condition. Next, we derive a lower bound from an upper one for quaternionic harmonic functions. These results generalize some of the classic results from the case of plane to the case of noncommutative quaterninionic half space. Copyright © 2017 John Wiley & Sons, Ltd. 相似文献
993.
As a first step towards the numerical analysis of the stochastic primitive equations of the atmosphere and the oceans,the time discretization of these equations by an implicit Euler scheme is studied.From the deterministic point of view,the 3D primitive equations are studied in their full form on a general domain and with physically realistic boundary conditions.From the probabilistic viewpoint,this paper deals with a wide class of nonlinear,state dependent,white noise forcings which may be interpreted in either the It6 or the Stratonovich sense.The proof of convergence of the Euler scheme,which is carried out within an abstract framework,covers the equations for the oceans,the atmosphere,the coupled oceanic-atmospheric system as well as other related geophysical equations.The authors obtain the existence of solutions which are weak in both the PDE and probabilistic sense,a result which is new by itself to the best of our knowledge. 相似文献
994.
The authors show that for any e ∈]0,1[,there exists an analytic outside zero solution to a uniformly elliptic conformal Hessian equation in a ball B C R5 which belongs to C1'ε(B) \ C1'ε+(B). 相似文献
995.
The article investigates the growth of multiple Dirichlet series.The lower order and the linear order of n-tuple Dirichlet series in C~n are defined and some relations between them and the coefficients and exponents of n-tuple Dirichlet series are obtained. 相似文献
996.
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998.
We consider a transmission problem consisting of two semilinear parabolic equations involving fractional diffusion operators of different orders in a general non-smooth setting with emphasis on Lipschitz interfaces and transmission conditions along the interface. We give a unified framework for the existence and uniqueness of strong and mild solutions, and their global regularity properties. 相似文献
999.
Monika Wolfmayr 《Numerical Methods for Partial Differential Equations》2017,33(2):403-424
In this work, new results on functional type a posteriori estimates for elliptic optimal control problems with control constraints are presented. More precisely, we derive new, sharp, guaranteed, and fully computable lower bounds for the cost functional in addition to the already existing upper bounds. Using both, the lower and the upper bounds, we arrive at two‐sided estimates for the cost functional. We prove that these bounds finally lead to sharp, guaranteed and fully computable upper estimates for the discretization error in the state and the control of the optimal control problem. First numerical tests are presented confirming the efficiency of the a posteriori estimates derived. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 403–424, 2017 相似文献
1000.
Christopher C. Tisdell 《International Journal of Mathematical Education in Science & Technology》2017,48(5):794-801
Knowing an equation has a unique solution is important from both a modelling and theoretical point of view. For over 70 years, the approach to learning and teaching ‘well posedness’ of initial value problems (IVPs) for second- and higher-order ordinary differential equations has involved transforming the problem and its analysis to a first-order system of equations. We show that this excursion is unnecessary and present a direct approach regarding second- and higher-order problems that does not require an understanding of systems. 相似文献