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61.
用A的不变子空间作参数,给出了算子方程AX=XAX的全部解。当A是单射或稠值域时,或者当A是正规算子时,给出了算子方程AX=XA=XAX的全部解。我们还给出正规算子X是算子方程AX=XZ=XAX的解的充分必要条件。 相似文献
62.
Comment on “A Hierarchy of Integrable Nonlinear Lattice Equations and New Integrable Symplectic Map“
Comment on a recent paper on Commun. Theor. Phys. (Beijing, China) 38 (2002) pp. 523-528. 相似文献
63.
Antonio Vitolo 《Journal of Differential Equations》2003,194(1):166-184
This paper is concerned with the maximum principle for second-order linear elliptic equations in a wide generality. By means of a geometric condition previously stressed by Berestycki-Nirenberg-Varadhan, Cabré was very able to improve the classical ABP estimate obtaining the maximum principle also in unbounded domains, such as infinite strips and open connected cones with closure different from the whole space. Now we introduce a new geometric condition that extends the result to a more general class of domains including the complements of hypersurfaces, as for instance the cut plane. The methods developed here allow us to deal with complete second-order equations, where the admissible first-order term, forced to be zero in a preceding result with Cafagna, depends on the geometry of the domain. 相似文献
64.
65.
In this paper, by using elementary analysis, we establish some new Lyapunov-type inequalities for nonlinear systems of differential equations, special cases of which contain the well-known equations such as Emden-Fowler-type and half-linear equations. The inequalities obtained here can be used as handy tools in the study of qualitative behaviour of solutions of the associated equations. 相似文献
66.
Mohamed El-Gebeily Donal O'Regan 《Journal of Mathematical Analysis and Applications》2007,334(1):140-156
Existence theory is developed for the equation ?(u)=F(u), where ? is a formally self-adjoint singular second-order differential expression and F is nonlinear. The problem is treated in a Hilbert space and we do not require the operators induced by ? to have completely continuous resolvents. Nonlinear boundary conditions are allowed. Also, F is assumed to be weakly continuous and monotone at one point. Boundary behavior of functions associated with the domains of definitions of the operators associated with ? in the singular case is investigated. A special class of self-adjoint operators associated with ? is obtained. 相似文献
67.
In this paper we consider a class of nonlinear delay partial difference equations and a class of linear delay partial difference equations with variable coefficients, which may change sign. We obtain oscillation criteria for these equations. There are no results for the oscillation of these equations up to now. 相似文献
68.
Asymptotic methods for contact problems are expounded. Some typical integral equations are considered 相似文献
69.
A formulation of an implicit characteristic-flux-averaging method for the unsteady Euler equations with real gas effects is presented. Incorporation of a real gas into a general equation of state is achieved by considering the pressure as a function of density and specific internal energy. The Ricmann solver as well as the flux-split algorithm are modified by introducing the pressure derivatives with respect to density and internal energy. Expressions for calculating the values of the flow variables for a real gas at the cell faces are derived. The Jacobian matrices and the eigenvectors are defined for a general equation of state. The solution of the system of equations is obtained by using a mesh-sequencing method for acceleration of the convergence. Finally, a test case for a simple form of equation of state displays the differences from the corresponding solution for an ideal gas. 相似文献
70.
吴臻 《数学物理学报(B辑英文版)》2004,24(1):91-99
The existence and uniqueness results of fully coupled forward-backward stochastic differential equations with stopping time (unbounded) is obtained. One kind of comparison theorem for this kind of equations is also proved. 相似文献