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101.
In this paper, the author has given an existence theorem for the resonant equa-tion,-△pu=λ1|u|p-2u+f(u)+h(x), without any Landesman-Lazer conditions on h(x). 相似文献
102.
This article considers the Dirichlet problem of homogeneous and inhomogeneous second-order ordinary differential systems. A nondegeneracy result is proven for positive solutions of homogeneous systems. Sufficient and necessary conditions for the existence of multiple positive solutions for inhomogeneous systems are obtained by making use of the nondegeneracy and uniqueness results of homogeneous systems. 相似文献
103.
The signless Laplacian matrix of a graph is the sum of its diagonal matrix of vertex degrees and its adjacency matrix. Li and Feng gave some basic results on the largest eigenvalue and characteristic polynomial of adjacency matrix of a graph in 1979. In this paper, we translate these results into the signless Laplacian matrix of a graph and obtain the similar results. 相似文献
104.
研究对应于带特殊重试时间的M/M/1重试排队模型主算子在左半复平面的谱,证明-(2λ+α+β+√(α+β)^2+4λβ/4是该主算子的几何重数为1的特征值. 相似文献
105.
Gregoire Nadin 《Annali di Matematica Pura ed Applicata》2009,188(2):269-295
This paper deals with the generalized principal eigenvalue of the parabolic operator , where the coefficients are periodic in t and x. We give the definition of this eigenvalue and we prove that it can be approximated by a sequence of principal eigenvalues
associated to the same operator in a bounded domain, with periodicity in time and Dirichlet boundary conditions in space.
Next, we define a family of periodic principal eigenvalues associated with the operator and use it to give a characterization
of the generalized principal eigenvalue. Finally, we study the dependence of all these eigenvalues with respect to the coefficients.
相似文献
106.
We consider the Hamiltonian , describing the motion of one quantum particle on a three-dimensional lattice in an external field. We investigate the number
of eigenvalues and their arrangement depending on the value of the interaction energy for μ ≥ 0 and λ ≥ 0.
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 158, No. 3, pp. 425–443, March, 2009. 相似文献
107.
M. T. Teryokhin 《Russian Mathematics (Iz VUZ)》2009,53(8):60-68
In this paper we investigate the existence of limit cycles of a system of the second-order differential equations with a vector parameter.We propose a method for representing a solution as a sum of forms with respect to the initial value and the parameter; we call this technique the method of small forms. We establish the conditions under which a sufficiently small neighborhood of the equilibrium point contains no limit cycles. We construct a polynomial, whose positive roots of odd multiplicity define the lower bound for the number of cycles, and simple positive roots (other positive roots do not exist) define the number of limit cycles in a sufficiently small neighborhood of the equilibrium point.We prove theorems, whose conditions guarantee that a positive root of odd multiplicity defines a unique limit cycle, but a positive root of even multiplicity defines exactly two limit cycles.We propose a method for defining the type of the stability of limit cycles. 相似文献
108.
The pioneering works of Murat and Tartar (Topics in the mathematical modeling of composite materials. PNLDE 31. Birkhäuser, Basel, 1997) go a long way in showing, in general, that problems of optimal design may not admit solutions if microstructural designs are excluded from consideration. Therefore, assuming, tactilely, that the problem of minimizing the first eigenvalue of a two-phase conducting material with the conducting phases to be distributed in a fixed proportion in a given domain has no true solution in general domains, Cox and Lipton only study conditions for an optimal microstructural design (Cox and Lipton in Arch. Ration. Mech. Anal. 136:101–117, 1996). Although, the problem in one dimension has a solution (cf. Kre?n in AMS Transl. Ser. 2(1):163–187, 1955) and, in higher dimensions, the problem set in a ball can be deduced to have a radially symmetric solution (cf. Alvino et al. in Nonlinear Anal. TMA 13(2):185–220, 1989), these existence results have been regarded so far as being exceptional owing to complete symmetry. It is still not clear why the same problem in domains with partial symmetry should fail to have a solution which does not develop microstructure and respecting the symmetry of the domain. We hope to revive interest in this question by giving a new proof of the result in a ball using a simpler symmetrization result from Alvino and Trombetti (J. Math. Anal. Appl. 94:328–337, 1983). 相似文献
109.
Venkatramani Lakshmibai Komaranapuram N. Raghavan Parameswaran Sankaran 《Central European Journal of Mathematics》2009,7(2):214-223
It is shown that the proof by Mehta and Parameswaran of Wahl’s conjecture for Grassmannians in positive odd characteristics
also works for symplectic and orthogonal Grassmannians.
相似文献
110.