Uniqueness implies existence and uniqueness criterion for nonlocal boundary value problems for third order differential equations

For the third order differential equation, we consider uniqueness implies existence results for solutions satisfying the nonlocal -point boundary conditions, Uniqueness of solutions of such boundary value problems is intimately related to solutions of the third order equation satisfying certain nonlocal -point boundary conditions. These relationships are investigated as well.

     

一类Riemann-Hilbert边值逆问题

给出解析函数的一类R iem ann-H ilbert边值逆问题的数学提法,依据解析函数R iem ann-H ilbert边值问题的经典理论,讨论了此边值问题的可解性,给出了该边值问题的可解条件和解的表示式.     

Existence of solutions for a cantilever beam problem

We are concerned with the fourth-order nonuniform cantilever beam problem

(I(x)WΔ∇(x)⁾Δ∇=f(x,W(x)),     

Existence of multiple positive solutions for one-dimensional p-Laplacian

In this paper we consider the multipoint boundary value problem for one-dimensional p-Laplacian

     

Multiple fixed-sign solutions for a system of generalized right focal problems with deviating arguments

We consider the following system of generalized right focal boundary value problems

     

Existence and multiplicity of positive solutions for multi-parameter three-point differential equations system

In this paper, we study the existence and multiplicity of positive solutions for the differential equations system

     

Interior numerical approximation of boundary value problems with a distributional data

We study the approximation properties of a harmonic function u ∈ H^1?k(Ω), k > 0, on a relatively compact subset A of Ω, using the generalized finite element method (GFEM). If Ω = ??, for a smooth, bounded domain ??, we obtain that the GFEM‐approximation u_S ∈ S of u satisfies ‖u ? u_S‖ ≤ Ch^γ‖u‖, where h is the typical size of the “elements” defining the GFEM‐space S and γ ≥ 0 is such that the local approximation spaces contain all polynomials of degree k + γ. The main technical ingredient is an extension of the classical super‐approximation results of Nitsche and Schatz (Applicable Analysis 2 (1972), 161–168; Math Comput 28 (1974), 937–958). In addition to the usual “energy” Sobolev spaces H¹(??), we need also the duals of the Sobolev spaces H^m(??), m ∈ ?₊. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006     

Accurate Q value for the Se double-electron-capture decay

The Q   value of the neutrinoless double-electron-capture (0νECEC$0\nu \text{ECEC}$) decay of ⁷⁴Se was measured by using the JYFLTRAP Penning trap. The determined value is 1209.169(49) keV, which practically excludes the possibility of a complete energy degeneracy with the second ²⁺$2^{+}$ state (1204.205(7) keV) of ⁷⁴Ge in a resonant 0νECEC$0\nu \text{ECEC}$ decay. We have also computed the associated nuclear matrix element by using a microscopic nuclear model with realistic two-nucleon interactions. The computed matrix element is found to be quite small. The failure of the resonant condition, combined with the small nuclear matrix element and needed p-wave capture, suppresses the decay rate strongly and thus excludes ⁷⁴Se as a possible candidate to search for resonant 0νECEC$0\nu \text{ECEC}$ processes.     

An exact solution of the moving boundary problem for the expansion of a plasma cylinder in a magnetic field

An exact analytic solution has been obtained for a uniformly expanding, neutral, infinitely conducting plasma cylinder in an external uniform and constant magnetic field. The electrodynamical aspects related to the emission and transformation of energy have been considered as well. The results obtained can be used in analysing the recent experimental and simulation data.