By a sub-super solution argument, we study the existence of positive solutions for the system ⎧ in Ω, ⎪ in Ω, ⎨u,v > 0 in Ω, ⎩u = v = 0 on ∂Ω, where Ω is a bounded domain in with smooth boundary or . A nonexistence result is obtained for radially symmetric solutions.
The paper develops an explicit a priori error estimate for finite element solution to nonhomogeneous Neumann problems. For this purpose, the hypercircle over finite element spaces is constructed and the explicit upper bound of the constant in the trace theorem is given. Numerical examples are shown in the final section, which implies the proposed error estimate has the convergence rate as .
A necessary and sufficient condition is obtained for a discrete multiplicity variety to be an interpolating variety for the space .
We prove in this paper that a given discrete variety V in C is an interpolating variety for a weight p if and only if V is a subset of the variety {ξ ∈ C: f(ξ) = f(ξ) = ... = f(ξ) = 0} of m functions f, ..., f in the weighted space the sum of whose directional derivatives in absolute value is not less than ε exp(-C(ζ)), ζ ∈ V for some constants ε, C > 0. The necessary and sufficient conditions will be also given in terms of the Jacobian matrix of f, ..., f. As a corollary, we solve an open...
The paper deals with error estimates and lower bound approximations of the Steklov eigenvalue problems on convex or concave domains by nonconforming finite element methods. We consider four types of nonconforming finite elements: Crouzeix-Raviart, , and enriched Crouzeix-Raviart. We first derive error estimates for the nonconforming finite element approximations of the Steklov eigenvalue problem and then give the analysis of lower bound approximations. Some numerical results are presented to...
In this paper, we revisit the artificial potential based approach in the flocking control for multi-agent systems, where our main concerns are migration and trajectory tracking problems. The static destination or, more generally, the moving reference point is modeled by a virtual leader, whose information is utilized by some agents, called active agents (AA), for the controller design. We study a decentralized flocking controller for the case where the set of AAs is fixed. Some results on the velocity...
In this paper, we investigate the value distribution of meromorphic solutions of homogeneous and non-homogeneous complex linear differential-difference equations, and obtain the results on the relations between the order of the solutions and the convergence exponents of the zeros, poles, a-points and small function value points of the solutions, which show the relations in the case of non-homogeneous equations are sharper than the ones in the case of homogeneous equations.
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