共查询到20条相似文献,搜索用时 31 毫秒
1.
G.R. Nicklason 《Journal of Mathematical Analysis and Applications》2009,358(1):75-80
We consider the classical Poincaré problem of a linear center perturbed by homogeneous polynomials of degree n?2. Using certain parity properties of a related differential equation, we develop a technique for obtaining center conditions for an arbitrary value of n and use it to exhibit explicitly new center conditions for n=4,…,8. 相似文献
2.
A. M. Akhtyamov 《Differential Equations》2014,50(4):546-547
We consider a boundary value problem for an ordinary differential equation of order n with a spectral parameter in n boundary conditions. We suggest a method for changing one of the boundary conditions so as to make the problem have a prescribed spectrum. 相似文献
3.
J. Feuer 《Journal of Mathematical Analysis and Applications》2003,288(1):147-160
We investigate the periodic nature of solutions of a “max-type” difference equation sometimes referred to as the “Lyness max” equation. The equation we consider is xn+1=max{xn,A}/xn−1, n=0,1,…, where A is a positive real parameter and the initial conditions are arbitrary positive numbers. We also present related results for a similar equation sometimes referred to as the “period 7 max” equation. 相似文献
4.
Victor Tkachenko 《Journal of Mathematical Analysis and Applications》2005,303(1):173-187
We present several conditions sufficient for global stability of the zero solution of nonautonomous difference equation xn+1=qxn+fn(xn,…,xn−k), n∈Z, when the nonlinearities fn satisfy a sort of negative feedback condition. Moreover, for every k∈N, we indicate qk such that one of our stability conditions is sharp if q∈(0,qk]. We apply our results to discrete versions of Nicholson's blowflies equation, the Mackey-Glass equations, and the Wazewska and Lasota equation. 相似文献
5.
Gary D. Jones 《Journal of Mathematical Analysis and Applications》2002,269(2):454-461
Solutions of an nth order differential inequality with n boundary conditions are compared to solutions of an nth order disconjugate differential equation. It is shown the ratios of certain of these solutions are monotone. 相似文献
6.
In this paper we prove the existence and uniqueness of solutions to the initial value problems associated with the GRID integro-differential equation describing macroscopic growth of an organism. We consider the general form of the macroscopic growth operator Φ and study the set of conditions on Φ that are sufficient to guarantee existence and uniqueness of solutions in Rn,n=1,2,3. 相似文献
7.
V. Zh. Dumanyan 《Theoretical and Mathematical Physics》2014,180(2):917-931
In our preceding papers, we obtained necessary and sufficient conditions for the existence of an (n?1)-dimensionally continuous solution of the Dirichlet problem in a bounded domain Q ? ? n under natural restrictions imposed on the coefficients of the general second-order elliptic equation, but these conditions were formulated in terms of an auxiliary operator equation in a special Hilbert space and are difficult to verify. We here obtain necessary and sufficient conditions for the problem solvability in terms of the initial problem for a somewhat narrower class of right-hand sides of the equation and also prove that the obtained conditions become the solvability conditions in the space W 2 1 (Q) under the additional requirement that the boundary function belongs to the space W 2 1/2 (?Q). 相似文献
8.
Kh. D. Ikramov 《Mathematical Notes》2016,100(5-6):720-723
Consider the sesquilinearmatrix equation X*DX + AX + X*B + C = 0, where all the matrices are square and have the same order n. With this equation, we associate a block matrix M of double order 2n. The solvability of the above equation turns out to be related to the existence of n-dimensional neutral subspaces for the matrix M. We indicate sufficiently general conditions ensuring the existence of such subspaces. 相似文献
9.
M. A. Komarov 《Siberian Mathematical Journal》2014,55(4):611-621
Using reduction to polynomial interpolation, we study the multiple interpolation problem by simple partial fractions. Algebraic conditions are obtained for the solvability and the unique solvability of the problem. We introduce the notion of generalized multiple interpolation by simple partial fractions of order ≤ n. The incomplete interpolation problems (i.e., the interpolation problems with the total multiplicity of nodes strictly less than n) are considered; the unimprovable value of the total multiplicity of nodes is found for which the incomplete problem is surely solvable. We obtain an order n differential equation whose solution set coincides with the set of all simple partial fractions of order ≤ n. 相似文献
10.
We study the boundary exact controllability for the semilinear Schrödinger equation defined on an open, bounded, connected set Ω of a complete, n-dimensional, Riemannian manifold M with metric g. We prove the locally exact controllability around the equilibria under some checkable geometrical conditions. Our results show that exact controllability is geometrical characters of a Riemannian metric, given by the coefficients and equilibria of the semilinear Schrödinger equation. We then establish the globally exact controllability in such a way that the state of the semilinear Schrödinger equation moves from an equilibrium in one location to an equilibrium in another location. 相似文献
11.
A. Laradji 《Journal of Differential Equations》2018,264(8):5480-5488
We provide necessary and sufficient conditions for which an nth-order linear differential equation has a general polynomial solution. We also give necessary conditions that can directly be ascertained from the coefficient functions of the equation. 相似文献
12.
We obtain existence conditions and asymptotic, as t → ω (ω ≤ +∞), representations of a certain class of monotone solutions of an nth-order differential equation whose right-hand side is a sum of terms with regularly varying nonlinearities. 相似文献
13.
A. Duane Porter 《Linear algebra and its applications》1976,13(3):177-184
Let A be an n×s matrix of rank r, B be an n×t matrix of rank ρ?r, and X be an s×t matrix. This paper discusses conditions on the matrices A and B so that the matric equation AX=B will have solutions for the matrix X. 相似文献
14.
A. S. Makin 《Differential Equations》2013,49(5):536-544
We consider a spectral problem generated by a Sturm-Liouville equation on the interval (0, π) with degenerate boundary conditions. We prove the existence of potentials q(x) ∈ L 2(0, π) such that the multiplicities of the eigenvalues λ n monotonically tend to infinity as n → ∞. 相似文献
15.
Jean-Paul Penot Constantin Z?linescu 《Journal of Mathematical Analysis and Applications》2008,347(1):188-203
Given a convergent sequence of Hamiltonians (Hn) and a convergent sequence of initial data (gn) for the first-order evolutionary Hamilton-Jacobi equation, we look for conditions ensuring that the sequences (un) and (vn) of Lax solutions and Hopf solutions respectively converge. The convergences we deal with are variational convergences. We take advantage of several recent results giving criteria for the continuity of usual operations. 相似文献
16.
Doron Zeilberger 《Discrete Mathematics》1980,31(1):65-77
Various discrete functions encountered in Combinatorics are solutions of Partial Difference Equations in the subset of Nn given by m1?m2???mn?0. Given a partial difference equation, it is described how to pass from the standard “easy” solution of an equation in Nn to a solution of the same equation subject to certain “Dirichlet” or “Neumann” boundary conditions in the domain m1?m2???mn?0 and related domains. Applications include a rather quick derivation of MacMahon's generating function for plane partitions, a generalization and q-analog of the Ballot problem, and a joint analog of the Ballot problem and Simon Newcomb's problem. 相似文献
17.
Luc Haine Didier Vanderstichelen 《Journal of Computational and Applied Mathematics》2011,236(1):19-27
We consider the 2-dimensional Toda lattice tau functions τn(t,s;η,θ) deforming the probabilities τn(η,θ) that a randomly chosen matrix from the unitary group U(n), for the Haar measure, has no eigenvalues within an arc (η,θ) of the unit circle. We show that these tau functions satisfy a centerless Virasoro algebra of constraints, with a boundary part in the sense of Adler, Shiota and van Moerbeke. As an application, we obtain a new derivation of a differential equation due to Tracy and Widom, satisfied by these probabilities, linking it to the Painlevé VI equation. 相似文献
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Robert M. Yamaleev 《Journal of Mathematical Analysis and Applications》2006,322(2):815-824
Generator of the complex algebra within the framework of general formulation obeys the quadratic equation. In this paper we explore multicomplex algebra with the generator obeying n-order polynomial equation with real coefficients. This algebra induces generalized trigonometry ((n+1)-gonometry), underlies of the nth order oscillator model and nth order Hamilton equations. The solution of an evolution equation generated by (n×n) matrix is represented via the set of (n+1)-gonometric functions. The general form of the first constant of motion of the evolution equation is established. 相似文献