SOME ANALYTIC TOOLS USED IN THE INVESTIGATION OF SOLVABILITY OF BOUNDARY VALUE PROBLEMS FOR A B ELLI...

boundary value problems,” Applied Mathematics and Computation, vol. 203, no. 1, pp. 30–38, 2008.
20 D. Bai and Y. Xu, “Nontrivial solutions of boundary value problems of second-order difference
equations,” Journal of Mathematic[r]

Calculation of eigenvalue problems for the secondorder ordinary differential equations is relevant for the physics problems. The secondorder ordinary differential equation with homogeneous Dirichlet boundary condition was considered. The Chebyshev pseudospectral method (CPM) was used for the problem[r]

letter c is used throughout to denote a positive constant, not necessarily the same at each occurrence.
Since Ω is compact, ∂ Ω can be covered by a finite number of neighbourhoods V of its points. It is enough to prove the better regularity of<[r]

Definition 1.1. The set Ᏺ is said to be quasiequicontinuous in [0, c ] if for any ε > 0 there
exists δ > 0 such that if x ∈ Ᏺ , k ∈ Z , t ∗ , t ∗∗ ∈ ( t k − 1, t k ] ∩ [0, c ], and | t ∗ − t ∗∗ | < δ , then
| x ( t ∗ ) − x ( t ∗∗ ) | < ε .
Lemma 1.2 (compactnes[r]

n
i = 1 α i u(η i ), and n
i = 1 α i ≤ 1 for the purpose of establishing existence results. We will de- termine su ffi cient conditions on our function f such that the assumptions of the fixed point theorem are satisfied, which in return gives us the<[r]

investigate the existence of solutions to the problem by means of di ff erential inequalities and Schaefer fixed point theorem. Their results complement and extend those of [ 22 , 23 ] in the sense that they allow superlinear growth of the<[r]

In this report, we examine the unsteady Stokes equations with nonhomogeneous boundary conditions. As an application of a Carleman estimate, we first establish log type stabilities for the solution of the equations from either an interior measurement of the velocity, or a boundary observation dependi[r]

Another approach is known, which is opposite in a sense. When solving the problem of linear conjugation with a measurable bounded coe ffi cient G in the explicit form, in this or other way, not making use of the boundedness results,[r]

z n −→ w z in D , then K ( z n ) → K ( z ) in C and N : C → P wkc ( D ) is usc from C , furnished with the strong topology into D , furnished with the weak topology.
Theorem 2.1. If C, D, and G = K ◦ N are as above, 0 ∈ C, and G is compact (namely, G maps bounded subset[r]

by using a functional-type cone expansion–compression fixed-point theorem, the author gets the existence of at least one positive solution to BVP (1.3), (1.4) and BVP (1.3), (1.5).
However, to the best of the authors’ knowledge, up to now, there are[r]

∞ , ∞ ) for the 3D Boussinesq system with partial viscosity. Later, in [3] Zhou and Fan studied the Cauchy problem of certain Boussinesq − α equations in n dimensions with n = 2 or 3. We establish regularity for the solution under ∇ u ∈[r]

by using a functional-type cone expansion–compression fixed-point theorem, the author gets the existence of at least one positive solution to BVP (1.3), (1.4) and BVP (1.3), (1.5).
However, to the best of the authors’ knowledge, up to now, there are[r]

L 2 + ( k ∂ t u k L 2 k∇ φ k L ∞ + k µ k L ∞ k∇ ∂ t φ k L 2 + k ∂ t θ k L 2 ) k ∂ t u k L 2
≤ k∇ u k L ∞ k ∂ t u k 2 L 2 + C ( k ∆ ∂ t φ k L 2 + k ∂ t ( φ 3 − φ ) k L 2 + k∇ ∂ t φ k L 2 + 1) k ∂ t u k L 2 ,
which implies
k ∂ t u k L ∞ (0 ,T ; L 2 ) + k ∂ t u k L 2 (0 ,T ; H 1 ) ≤ C. (2.23) Usi[r]

regulators with greater assurance of a company’s ability to deal with potential risks, and can beneficially affect the extent and level of direct regulatory oversight.
The purpose of this document is to offer a systematic approach to quality risk[r]

Vietnam National University, 334 Nguyen Trai, Hanoi, Vietnam
Received May 12, 2004 Revised August 28, 2005
Abstract. In this paper we study the existence of weak solutions of the Dirichlet problem for a system of semilinear elliptic[r]

are finite. In all these cases, he also assumed that f ( u ) is either bounded above or below by a constant multiple of | u | in certain specified intervals. The techniques used in this paper can easily be extended to generalize these results.
(2) W[r]

In this paper, we study the Neumann boundary value problems without initial condition for Hyperbolic systems in cylinders. The main obtained results are the uniqueness and the existence of generalized solutions.