doi: 10.1080/00036819508840386pmid: N/A
We prove that there is a global attractor for in where the damping function P is monotone and allowed to be bounded.
doi: 10.1080/00036819508840387pmid: N/A
Topological results are applied to boundary value problems modeling nonlinear beams. A classical continuation theorem is used to prove existence results. Unified proofs,where possible, are given for all the physically relevant boundary conditions. A uniqueness result is given for the case of both ends simply supported.
Allegretto, W.; Xie, H.; Yang, Shixin
doi: 10.1080/00036819508840388pmid: N/A
Existence and partial uniqueness results are established,under a variety of conditions, for a system of equations arising in electrochemistry problems. The main idea is the reduction of the system to a single equation involving nonlocal terms. Upper and lower solution procedures are then applied to show both existence and uniqueness. In this way, results are obtained in more than one space dimension.
doi: 10.1080/00036819508840389pmid: N/A
The definition of integral transforms of the type as weak functions in the terminology of Lighthi117 and Jones4 is obtained. With respect to the theory of Fourier integral operators, both the amplitude function h and the phase function ψ vary in the Hörmander classes2, but the phase ψ, satisfies conditions less restrictive than the ones used by Traves12. Some concrete examples of h are given such as a good function as in Jones4 so that the class of the amplitude functions h ends up to be wide. The interdependence between the parameter of the phase function ψ, and the positivity condition required is also studied. More specific phase functions are used than the ones by Trbves12, in a way that our results can become more concrete. Some properties concerning the derivatives of the considered weak functions are also discussed.
Gopalsamy, K.; Li, Jibin; He, Xue-Zhong
doi: 10.1080/00036819508840390pmid: N/A
In this paper we point out the main idea to yield periodic solutions of Kaplan-Yorke type of differential delay equations. Some new sufficient conditions for the existence of Kaplan-Yorke type periodic solutions have been given. Many interesting examples are also disscused.
doi: 10.1080/00036819508840391pmid: N/A
We consider a second order system of partial differential equations of mixed hyperbolic-elliptic type on a domain bounded by two differentiable curves AC and BC in the hyperbolic region and a non-selfintersecting piecewise differentiabe curve I' connecting A to B in the elliptic region. AC and BC are either characteristic curves or satisfy certain simple inequalities with regard to the leading coefficients. We derive an apriori estimate for the system of differential operators for a certain class of functions with Dirichlet boundary condition on BC and part of and Neuman condition on the other part of r. The corresponding boundary value problem is formulated with uniqueness of a solution following directly from the apriori estimate.
doi: 10.1080/00036819508840392pmid: N/A
In this paper we derive the L,-saturation classes, 1 < p < ∞, of linear combinations of the so-called BDT-operators. For the proof we use an explicit Voronovskaja-type result which we proved in [13, Theorem 3.1, Theorem 3.21].
doi: 10.1080/00036819508840393pmid: N/A
Let Lj, j = 1,. . . ,J, be a finite number of closed linear subspaces of a Hilbert space, and let Pj be the orthogonal projections onto Lj. Let s be an infinite sequence (j1, j2,. . . ) of natural numbers jk with such that, for each j with , there are infinite k satisfying jk = j. For an element x0 of the space, set It is known, by Amemiya and Ando [1], that xk converges weakly to the orthogonal projection of xO onto . We shall show that if s is quasi-periodic, then xk converges strongly.
doi: 10.1080/00036819508840395pmid: N/A
We First define a continuous extension of the Laquerre polynomials and give some properties of this continuous extension. Then we define a continuous Laguerre transform for square integrable functions, give some properties of this transform and give a sampling theorem that is similar to the well known Shannon-Whittaker Sampling Theorem for Fourier transform. The inverse of this transform is also given.
doi: 10.1080/00036819508840396pmid: N/A
The well-known method of quasilinearization proved by Bellman and Kalaba [1,2] is extended to hyperbolic partial differential equations of the first order. The technic involves the application of lower and upper solutions and differential inequalities. The conclusion obtained includes non-convex fimctions thus extending the results for a larger class of functions. The upper and lower sequences converge to the unique solution quadratically.
Showing 1 to 10 of 26 Articles