Classical solution

In this paper, we have investigated the non-existence of positive solutions to the functional inequality involving the Laplace operator of order m on the punctured ball in Rn, where n > 2m ≥ 4.

6p vibenya 31-12-2024 1 0   Download

In this chapter, the following content will be discussed: Background, the critical-section problem, peterson’s solution, synchronization hardware, mutex locks, semaphores, classic problems of synchronization, monitors, synchronization examples, alternative approaches.

66p dien_vi02 07-10-2018 28 0   Download

In this paper, harmonic forced vibration of circular functionally graded plate integrated with two uniformly distributed actuator faces made of piezoelectric material is studied.

12p tohitohi 19-05-2020 15 1   Download

We obtain global well-posedness, scattering, and global L10 spacetime t,x bounds for energy-class solutions to the quintic defocusing Schr¨dinger equao tion in R1+3 , which is energy-critical. In particular, this establishes global existence of classical solutions. Our work extends the results of Bourgain [4] and Grillakis [20], which handled the radial case.

100p dontetvui 17-01-2013 50 6   Download

Poincar´ made the first attempt in 1896 on applying variational calculus e to the three-body problem and observed that collision orbits do not necessarily have higher values of action than classical solutions. Little progress had been made on resolving this difficulty until a recent breakthrough by Chenciner and Montgomery. Afterward, variational methods were successfully applied to the N -body problem to construct new classes of solutions.

25p dontetvui 17-01-2013 39 6   Download

In the first three parts of this series, we considered quadratic, cubic and quartic rings (i.e., rings free of ranks 2, 3, and 4 over Z) respectively, and found that various algebraic structures involving these rings could be completely parametrized by the integer orbits of an appropriate group representation on a vector space. These orbit results are summarized in Table 1.

43p dontetvui 17-01-2013 45 6   Download

This is the first in a series of papers in which we initiate the study of very rough solutions to the initial value problem for the Einstein-vacuum equations expressed relative to wave coordinates. By very rough we mean solutions which cannot be constructed by the classical techniques of energy estimates and Sobolev inequalities. Following [Kl-Ro] we develop new analytic methods based on Strichartz-type inequalities which result in a gain of half a derivative relative to the classical result. ...

52p noel_noel 17-01-2013 61 5   Download

This is the second in a series of three papers in which we initiate the study of very rough solutions to the initial value problem for the Einstein vacuum equations expressed relative to wave coordinates. By very rough we mean solutions which cannot be constructed by the classical techniques of energy estimates and Sobolev inequalities. In this paper we develop the geometric analysis of the Eikonal equation for microlocalized rough Einstein metrics. This is a crucial step in the derivation of the decay estimates needed in the first paper. ...

50p noel_noel 17-01-2013 56 5   Download

We introduce and study “isomonodromy” transformations of the matrix linear difference equation Y (z + 1) = A(z)Y (z) with polynomial A(z). Our main result is construction of an isomonodromy action of Zm(n+1)−1 on the space of coefficients A(z) (here m is the size of matrices and n is the degree of A(z)). The (birational) action of certain rank n subgroups can be described by difference analogs of the classical Schlesinger equations, and we prove that for generic initial conditions these difference Schlesinger equations have a unique solution. ...

43p tuanloccuoi 04-01-2013 66 7   Download

Surfaces of sections are a classical tool in the study of 3-dimensional dynamical systems. Their use goes back to the work of Poincar´ and Birkhoff. e In the present paper we give a natural generalization of this concept by constructing a system of transversal sections in the complement of finitely many distinguished periodic solutions. Such a system is established for nondegenerate Reeb flows on the tight 3-sphere by means of pseudoholomorphic curves.

134p tuanloccuoi 04-01-2013 63 8   Download

A MODIFIED QUASI-BOUNDARY VALUE METHOD FOR A CLASS OF ABSTRACT PARABOLIC ILL-POSED PROBLEMS M. DENCHE AND S. DJEZZAR Received 14 October 2004; Accepted 9 August 2005 We study a final value problem for first-order abstract differential equation with positive self-adjoint unbounded operator coefficient. This problem is ill-posed. Perturbing the final condition, we obtain an approximate nonlocal problem depending on a small parameter. We show that the approximate problems are well posed and that their solutions converge if and only if the original problem has a classical solution.

8p sting12 10-03-2012 73 4   Download

MULTIPLICITY RESULTS FOR A CLASS OF ASYMMETRIC WEAKLY COUPLED SYSTEMS OF SECOND-ORDER ORDINARY DIFFERENTIAL EQUATIONS FRANCESCA DALBONO AND P. J. MCKENNA Received 1 November 2004 We prove the existence and multiplicity of solutions to a two-point boundary value problem associated to a weakly coupled system of asymmetric second-order equations. Applying a classical change of variables, we transform the initial problem into an equivalent problem whose solutions can be characterized by their nodal properties.

23p sting12 10-03-2012 40 7   Download