共查询到20条相似文献,搜索用时 31 毫秒
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In this paper we obtain new conditions for the global existence and boundedness of solutions for nonlinear second-order equations of the form where is a real constant. The results are applicable to well-known Emden–Fowler and Lienard type equations. An illustrative example is also provided. 相似文献
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Lump solutions are analytical rational function solutions localized in all directions in space. We analyze a class of lump solutions, generated from quadratic functions, to nonlinear partial differential equations. The basis of success is the Hirota bilinear formulation and the primary object is the class of positive multivariate quadratic functions. A complete determination of quadratic functions positive in space and time is given, and positive quadratic functions are characterized as sums of squares of linear functions. Necessary and sufficient conditions for positive quadratic functions to solve Hirota bilinear equations are presented, and such polynomial solutions yield lump solutions to nonlinear partial differential equations under the dependent variable transformations and , where x is one spatial variable. Applications are made for a few generalized KP and BKP equations. 相似文献
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Weighted pseudo-almost periodic solutions of a class of semilinear fractional differential equations
Ravi P. Agarwal Bruno de Andrade Claudio Cuevas 《Nonlinear Analysis: Real World Applications》2010,11(5):3532-3554
We study the existence and uniqueness of a weighted pseudo-almost periodic (mild) solution to the semilinear fractional equation , , where is a linear operator of sectorial negative type. This article also deals with the existence of these types of solutions to abstract partial evolution equations. 相似文献
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Jianxi Liu 《Discrete Applied Mathematics》2013,161(16-17):2544-2548
The Randi? index of a graph is defined by , where is the degree of a vertex and the summation extends over all edges of . Delorme et al. (2002) [6] put forward a conjecture concerning the minimum Randi? index among all-vertex connected graphs with the minimum degree at least . In this work, we show that the conjecture is true given the graph contains vertices of degree . Further, it is true among -trees. 相似文献
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For a set of vertices of a graph , a vertex in , and a vertex in , let be the distance of and in the graph . Dankelmann et al. (2009) define to be an exponential dominating set of if for every vertex in , where . Inspired by this notion, we define to be an exponential independent set of if for every vertex in , and the exponential independence number of as the maximum order of an exponential independent set of .Similarly as for exponential domination, the non-local nature of exponential independence leads to many interesting effects and challenges. Our results comprise exact values for special graphs as well as tight bounds and the corresponding extremal graphs. Furthermore, we characterize all graphs for which equals the independence number for every induced subgraph of , and we give an explicit characterization of all trees with . 相似文献
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《Nonlinear Analysis: Hybrid Systems》2007,1(1):124-134
Convolution complementarity problems have the form: given a kernel function and a function , find a function such that , for (almost) all , and where . A fractional index problem of this kind has for small, with . Such problems are shown to have unique solutions under mild conditions. 相似文献
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The 2D -Navier–Stokes equations have the form with the continuity equation in a bounded domain where is a smooth real valued function defined on . We use the method described by Roh [J. Roh, -Navier Stokes equations, Ph.D. Thesis, University of Minnesota, 2001] for the derivation of -Kelvin–Voight equations represented by We discuss the existence and uniqueness of weak solutions of -Kelvin–Voight equations by the use of the well known Feado–Galerkin method. 相似文献
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《Applied Mathematics Letters》2005,18(11):1256-1264
In this paper, we discuss the existence of positive periodic solutions to the nonlinear differential equation where is an -periodic continuous function with , is continuous and is also an -periodic function for each . Using the fixed point index theory in a cone, we get an essential existence result because of its involving the first positive eigenvalue of the linear equation with regard to the above equation. 相似文献