共查询到20条相似文献,搜索用时 31 毫秒
1.
In this paper, we study solution structures of the following generalized Lennard-Jones system in R~n,x=(-α/|x|~(α+2)+β/|x|~(β+2))x,with 0 α β. Considering periodic solutions with zero angular momentum, we prove that the corresponding problem degenerates to 1-dimensional and possesses infinitely many periodic solutions which must be oscillating line solutions or constant solutions. Considering solutions with non-zero angular momentum, we compute Morse indices of the circular solutions first, and then apply the mountain pass theorem to show the existence of non-circular solutions with non-zero topological degrees. We further prove that besides circular solutions the system possesses in fact countably many periodic solutions with arbitrarily large topological degree, infinitely many quasi-periodic solutions, and infinitely many asymptotic solutions. 相似文献
2.
《Mathematical Methods in the Applied Sciences》2018,41(7):2769-2794
In this paper, we will establish the bounded solutions, periodic solutions, quasiperiodic solutions, almost periodic solutions, and almost automorphic solutions for linearly coupled complex cubic‐quintic Ginzburg‐Landau equations, under suitable conditions. The main difficulty is the nonlinear terms in the equations that are not Lipschitz‐continuity, traditional methods cannot deal with the difficulty in our problem. We overcome this difficulty by the Galerkin approach, energy estimate method, and refined inequality technique. 相似文献
3.
《Applied Mathematical Modelling》2014,38(19-20):4694-4704
We investigate the existence of “front” solutions of the saturation equation of two-phase flow in porous media. By front solution we mean a monotonic solution connecting two different saturations. The Brooks–Corey and the van Genuchten models are used to describe the relative-permeability – and capillary pressure–saturation relationships. We show that two classes of front solutions exist: self-similar front solutions and travelling-wave front solutions. Self-similar front solutions exist only for horizontal displacements of fluids (without gravity). However, travelling-wave front solutions exist for both horizontal and vertical (including gravity) displacements. The stability of front solutions is confirmed numerically. 相似文献
4.
Abdul‐Majid Wazwaz 《Mathematical Methods in the Applied Sciences》2017,40(6):2277-2283
In this work, we study the two‐mode Korteweg–de Vries (TKdV) equation, which describes the propagation of two different waves modes simultaneously. We show that the TKdV equation gives multiple soliton solutions for specific values of the nonlinearity and dispersion parameters involved in the equation. We also derive other distinct exact solutions for general values of these parameters. We apply the simplified Hirota's method to study the specific of the parameters, which gives multiple soliton solutions. We also use the tanh/coth method and the tan/cot method to obtain other set of solutions with distinct physical structures. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
5.
In this paper we address bargaining games where the agents have to take into account different criteria to value the decisions.
We propose the class of generalized maximin solutions, as the natural extension for these games of the maximin solutions in
conventional bargaining. In order to refine this solution concept, we define a multicriteria lexicographic partial ordering
and present the class of generalized leximin solutions as those that are nondominated with respect to this relation. We establish
some properties of these solutions and characterize them as solutions of multicriteria problems.
The research of the authors is partially supported by the Spanish Ministry of Science and Technology projects BFM2002-11282-E
and BEC2003-03111. 相似文献
6.
本文研究Dalvey-Stewartson方程组的整体解与自相似解的存在性.首先,运用Ba- nach不动点定理得到一个关于解整体存在性的一般性定理,然后把一类特殊的初始值用到该存在性结果上去从而得到自相似解存在的结论. 相似文献
7.
Fei Liang 《Applied mathematics and computation》2011,218(8):3993-3999
This paper deals with the blow-up of positive solutions for a nonlinear reaction-diffusion equation subject to nonlinear boundary conditions. We obtain the conditions under which the solutions may exist globally or blow up in finite time. Moreover, an upper bound of the blow-up time, an upper estimate of the blow-up rate, and an upper estimate of the global solutions are given. At last we give two examples to which the theorems obtained in the paper may be applied. 相似文献
8.
This paper studies the problem of uniformly dissipative solutions of somefifth order non-linear differential equations by the use of frequency domaintechnique. We use the generalized theorem of Yacubovich on dissipativity toobtain some new sufficient conditions of the existence of solutions that aredissipative for (1.1) and (1.2). 相似文献
9.
Liu Yicheng Li Zhixiang 《Annals of Differential Equations》2005,21(3):362-365
We study the periodicity of the positive solutions of a class of difference equations with maximum. We prove that every positive solutions of these equations are eventually periodic. 相似文献
10.
《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2020,37(5):1109-1141
We study radial sign-changing solutions of a class of fully nonlinear elliptic Dirichlet problems in a ball, driven by the extremal Pucci's operators and with a power nonlinear term. We first determine a new critical exponent related to the existence or nonexistence of such solutions. Then we analyze the asymptotic behavior of the radial nodal solutions as the exponents approach the critical values, showing that new concentration phenomena occur. Finally we define a suitable weighted energy for these solutions and compute its limit value. 相似文献
11.
Mohamed Hayek 《Applied mathematics and computation》2011,218(6):2407-2420
Based on the simplest equation method, we propose exact and traveling-wave solutions for a nonlinear convection-diffusion-reaction equation with power law nonlinearity. Such equation can be considered as a generalization of the Fisher equation and other well-known convection-diffusion-reaction equations. Two important cases are considered. The case of density-independent diffusion and the case of density-dependent diffusion. When the parameters of the equation are constant, the Bernoulli equation is used as the simplest equation. This leads to new traveling-wave solutions. Moreover, some wavefront solutions can be derived from the traveling-wave ones. The case of time-dependent velocity in the convection term is studied also. We derive exact solutions of the equations by using the Riccati equation as simplest equation. The exact and traveling-wave solutions presented in this paper can be used to explain many biological and physical phenomena. 相似文献
12.
Convergence of Monotone Iterations for Differential Problem 总被引:4,自引:0,他引:4
Tadeusz Jankowski 《数学学报(英文版)》2000,16(4):711-720
We use the method of lower and upper solutions combined with monotone iterations to differential problems with a parameter.
Existence of extremal solutions to such problems is proved.
Received April 15, 1999, Revised December 6, 1999, Accepted July 18, 2000 相似文献
13.
Periodic solutions of abstract functional differential equations with state‐dependent delay 下载免费PDF全文
Filipe Andrade Claudio Cuevas Hernán R. Henríquez 《Mathematical Methods in the Applied Sciences》2016,39(13):3897-3909
In this paper, we are concerned with the existence of solutions of systems determined by abstract functional differential equations with infinite and state‐dependent delay. We establish the existence of mild solutions and the existence of periodic solutions. Our results are based on local Lipschitz conditions of the involved functions. We apply our results to study the existence of periodic solutions of a partial differential equation with infinite and state‐dependent delay. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
14.
研究了一类具第三类功能反应且食饵具有避难所的非自治捕食系统.利用Lyapunov函数方法得到了系统持续生存的条件,以及在一定条件下,系统存在全局渐进稳定的周期正解.对于更广泛的概周期现象,也得到了存在唯一全局渐进稳定的概周期正解的充分条件. 相似文献
15.
We prove the existence and uniqueness of global strong solutions to the Cauchy problem of the three-dimensional magnetohydrodynamic equations in R3 when initial data are helically symmetric. Moreover, the large-time behavior of the strong solutions is obtained simultaneously. 相似文献
16.
Joelma Azevedo Claudio Cuevas Herme Soto 《Mathematical Methods in the Applied Sciences》2017,40(18):6944-6975
We investigate the asymptotic periodicity, Lp‐boundedness, classical (resp., strong) solutions, and the topological structure of solutions set of strongly damped semilinear wave equations. The theoretical results are well complemented with a set of very illustrating applications. 相似文献
17.
This paper introduces and analyzes the class of inequality averse multi-utilitarian solutions for cooperative bargaining problems.
We show that generalized Gini solutions and inequality averse Choquet solutions are particular cases of this new multi-valued
solution concept and provide a complete characterization in which an invariance property, consisting of a weakening of both
the linear invariance axiom in Blackorby et al. (Econometrica 62:1161–1178, 1994) and the restricted invariance axiom in Ok
and Zhou (Games Econ Behav 33:249–264, 2000), plays an important role. Moreover, by relaxing the assumptions involved in the
characterization, the class is extended to include inequality loving multi-utilitarian solutions which are also studied in
the paper. 相似文献
18.
We study radially symmetric classical solutions of the Dirichlet problem for a heat equation with a supercritical nonlinear source. We give a sufficient condition under which blow-up in infinite time cannot occur. This condition involves only the growth rate of the source term at infinity. We do not need the homogeneity property which played a key role in previous proofs of similar results. We also establish the blow-up rate for a class of solutions which blow up in finite time. 相似文献
19.
A study on a two‐wave mode Kadomtsev–Petviashvili equation: conditions for multiple soliton solutions to exist 下载免费PDF全文
Abdul‐Majid Wazwaz 《Mathematical Methods in the Applied Sciences》2017,40(11):4128-4133
We establish a two‐wave mode equation for the integrable Kadomtsev–Petviashvili equation, which describes the propagation of two different wave modes in the same direction simultaneously. We determine the necessary conditions that make multiple soliton solutions exist for this new equation. The simplified Hirota's method will be used to conduct this work. We also use other techniques to obtain other set of periodic and singular solutions for the two‐mode Kadomtsev‐Petviashvili equation. Copyright © 2017 John Wiley & Sons, Ltd. 相似文献
20.
In this work we characterize objective functions which do not change the set of efficient solutions (weakly efficient solutions, properly efficient solutions). Necessary and sufficient conditions for an objective function to be weakly nonessential (properly nonessential) are presented. We establish relations between weakly nonessential, properly nonessential and nonessential functions. 相似文献