the hilbert boundary value problem

... due to the definition of matrix Q(k) Hence, there holds the following n Rutkauskas Boundary Value Problems 2011, 2011:16 http://www.boundaryvalueproblems.com/content/2011/1/16 Page of 11 Theorem ... in the opposite case The uniqueness of the solutions of both the problems D1 and D2 yields the following lemma Lemma Let v = (v1, v2, , vs) be a solution of problem D1 or problem D2 with the ... Rutkauskas Boundary Value Problems 2011, 2011:16 http://www.boundaryvalueproblems.com/content/2011/1/16 Page of 11 solved under the assumption that elements of the matrices Bi(x) tend...

Ngày tải lên: 21/06/2014, 00:20

... [23] From the first Green’s identity, the representation of the difference between the solutions to the initial value problem and the initial -boundary value problem can be established The only unknown ... modern mathematics In this thesis, We will focus on the one dimensional Navier-Stokes equations and consider the initial -boundary value problem There are a lot of works on the initial value problems ... recall the representation of H(x, y, t) which is the difference of the Green’s function for the initial -boundary value problem G(x, y, t) and the fundamental solution for the initial value problem...

Ngày tải lên: 09/09/2015, 10:15

... 0, 𝑐2 ∕= 0, (1.3) the problems are two-point BVPs; if 𝑏1 = 𝑐1 = 𝑎2 = 𝑏2 = 0, the problems are initial value problems; if 𝑏1 = 𝑎2 = 0, 𝑎1 = 𝑐1 ∕= 0, 𝑏2 = 𝑐2 ∕= 0, (1.4) the problems are periodic ... and effective Mathematics Subject Classification (2000) 35A24, 46E20, 47B32 Preprint submitted to Boundary Value Problems December 7, 2011 Introduction Initial and boundary value problems of ordinary ... kernel Hilbert spaces have been presented in the first step And in the second step, the homogeneous IBVPs is deal with in the RKHS Finally, one analytic approximation of the solutions of the second-order...

Ngày tải lên: 20/06/2014, 20:20

... {xq+1 } is the m solution of the boundary value problem (6) Examples In this section, we introduce three particular boundary value problems in the form of the system (1) The first problem is a ... convergence of the sequence (14) and the relation of the limit function to the solution of some additively modified boundary value problem Theorem Let the assumptions (A1)–(A4) be satisfied Then for ... unique solution of the Cauchy problem (16) Let us find a relation of the limit function x∗ = x∗ (t, z, λ) of the sequence {xm } and the solution of the parameterized boundary value problem (6) For...

Ngày tải lên: 20/06/2014, 21:20

... solutions depends on the amplitude of the range of the values assumed by the functions a and g in the interval [ν1, ν2] determined by the prescribed boundary values In Section we study the existence/non-existence ... glance on the role played by the behavior with respect to x The study of the solvability of the boundary value problem for rates of decay δ < -1 is still open Existence and non-existence theorems ... used only in the choice of the constant C (see (2.11)) and in the proof of Step Hence, we now present only the proof of this part, the rest being the same Cupini et al Boundary Value Problems 2011,...

Ngày tải lên: 20/06/2014, 22:20

... results on the regularity of solutions of elliptic boundary problems in smooth domains (see, e.g., [12]), we have Hung et al Boundary Value Problems 2011, 2011:17 http://www.boundaryvalueproblems.com/content/2011/1/17 ... article as: Hung et al.: On the regularity of the solution for the second initial boundary value problem for hyperbolic systems in domains with conical points Boundary Value Problems 2011 2011:17 Submit ... prove the main theorems of this section Theorem 3.3 Let h be a nonnegative integer Assume that all the coefficients apq together with their derivatives with respect to t are bounded on Q Then there...

Ngày tải lên: 21/06/2014, 00:20

... and the thesis holds.▀ Another related problem Now, we will consider a new non-classical initial -boundary value problem (P5) for the heat equation in the slab [0,1], which is related to the previous ... et al Boundary Value Problems 2011, 2011:4 http://www.boundaryvalueproblems.com/content/2011/1/4 Page 15 of 17 In this case, the function F depends on the evolution of the temperature of the temperature ... respectively, for the data fi, gi, hi and F (i = 1,2) in problem (P1) Then we obtain the following results Theorem Let us consider the problem (P1) under the assumptions (HA) to (HD), then we have:...

Ngày tải lên: 21/06/2014, 02:20

... three point boundary value problems via fixed point index theory Nonlinear Anal 2001, 47:4319-4332 Raffoul YN: Positive solutions of three-point nonlinear second order boundary value problem Electron ... completed the main part of this paper, SKN and LZ corrected the main theorems and gave two examples All authors read and approved the final manuscript Competing interests The authors declare that they ... mentioning that the conditions of our theorems are easily to verify, so they are applicable to a variety of problems, see Examples 4.1 and 4.2 The proof of our main results is based upon the following...

Ngày tải lên: 21/06/2014, 03:20

... 2 Boundary Value Problems The fact that ·, · M induces the equivalent norm to the standard norm of the Sobolev Hilbert space of Mth order follows from Poincar´ inequality Let us introduce the ... obtain the supremum of S i.e., the best constant of Sobolev inequality , we consider the following clamped boundary value problem: −1 M u 2M f x −s < x < s , BVP M u ±s i 0≤i≤M−1 Concerning the ... is the determinant of M × M matrix Ki x ∨ y max x, y j 2s −s < x, y < s ≤ i, j ≤ M − , x ∧ y 1.6 x, y , and Boundary Value Problems With the aid of Proposition 1.1, we obtain the following theorem...

Ngày tải lên: 21/06/2014, 05:20

... to the boundary value problem xΔΔ t λf t, xσ t , xΔ t , xΔ a 0, t ∈ a, ρ2 b Ì, x b Then the boundary value problem 1.2 has at least one solution in C2 a, b Proof The proof is the same as 18, Theorem ... 3.1 Then dynamic boundary value problem x∇∇ t g t, xρ t , x∇ t , x a 0, x∇ t ∈ σ a , b Ì, b 3.2 has at least one solution Remark 3.2 According to Theorem 3.1, the dynamic boundary value problem ... above The idea in 18 was from Kelevedjiev 19 , in which discussions were for boundary value problems of ordinary differential equation This paper studies the existence of solutions for the nonlinear...

Ngày tải lên: 21/06/2014, 05:20

... in Boundary Value Problems In this section, we aim to adopt the well-known Avery-Henderson fixed point theorem to prove the existence of at least two positive solutions in the boundary value problems ... establish the following result on the existence of at least three solutions in the boundary value problems 1.9 and 1.10 Theorem 4.2 Suppose that the hypotheses H1 – H3 are all fulfilled Assume that there ... to the following discussion Section analytically establishes the criteria for the existence of at least two positive solutions in the boundary value problems 1.9 and 1.10 with the aid of the...

Ngày tải lên: 21/06/2014, 11:20

... , Boundary Value Problems Formulation of the Boundary Value Problem For second-order equations with nonnegative characteristic form, Keldys and Fichera presented a kind of boundary that is the ... the Keldys-Fichera boundary value problem, with that the associated problem is of well-posedness However, for higher-order ones, the discussion of well-posed boundary value problem has not been ... 2.13 Boundary Value Problems We can see that the item 2.13 of boundary value condition is determined by the leading term matrix 2.2 , and 2.12 is defined by the odd term matrix 2.6 Moreover, if the...

Ngày tải lên: 21/06/2014, 11:20

... due to the fact that the infinite interval 0, ∞ is noncompact The following compactness criterion will help us to resolve this problem then E C∞ R , R Then, M is relatively compact in E if the following ... t Then, P1 1/2, Q1 positive solution 1/4, P1 2e−4t , q t −3t e 5.6 Q1 < By Theorem 4.2, BVP 5.4 has a unique unbounded 14 Boundary Value Problems Acknowledgments The authors are grateful to the ... generalizations of linear elliptic boundary value ı problems,” Doklady Akademii Nauk SSSR, vol 185, pp 739–740, 1969 V A II’in and E I Moiseev, “Nonlocal boundary value problem of the first kind for a Sturm-Liouville...

Ngày tải lên: 21/06/2014, 11:20

... contrast to the “standard” boundary conditions as the Dirichlet problem, Neumann problem, Robin problem, periodic boundary value problem 9–12 , for example In the problem considered; there is not ... of the √ We will write s O r when < lim → |s /r | < ∞ order O The situation in the case of nonlocal boundary value problem is complicated by the fact that there are the inner points in the boundary ... Such boundary value problems can also arise in the study of the steady-states of a heated bar with the thermostats, where the controllers at t a and t b maintain a temperature according to the...

Ngày tải lên: 21/06/2014, 11:20

... by Theorems 2.2 and 2.3, there exists a unique solution α1 of 3.16 such that α0 ≤ α1 ≤ β t , α1 ≤ M1 , t ∈ 0, 3.18 Boundary Value Problems Note that the uniqueness of the solution follows by Theorem ... are not the solutions of 3.60 and α t < β t , t ∈ 0, Also, the assumptions of Theorem 3.1 are satisfied Thus, the conclusion of Theorem 3.1 applies to the problem 3.60 Acknowledgment The author ... ∂2 ∂x∂x x −y ∂2 ∂x 3.1 Boundary Value Problems Then, there exists a monotone sequence {αn } of approximate solutions converging uniformly to a unique solution of the problems 1.1 - 1.2 Proof...

Ngày tải lên: 21/06/2014, 11:20

... Equations author studied the existence of solutions for the nonlinear boundary value problem by using Krasnoselskii’s fixed point theorem and Leggett and Williams fixed point theorem, respectively ... βi u θi u i They established a corresponding iterative scheme for the problem by using the monotone iterative technique All the above works were done under the assumption that the nonlinear ... condition H1 holds, then for h ∈ Cld 0, T φp uΔ∇ m−2 bi u ξi , u0 ∇ h t Δ u T 0, the boundary value problem (BVP) t ∈ 0, T 0, φp u Tκ , Δ∇ Tκ , m−2 ci φp u i 2.8 Δ∇ ξi i has the unique solution...

Ngày tải lên: 21/06/2014, 20:20

... fixed point theory 1, 3, 5–7 , the method of upper and lower solutions , and critical point theory 9, 10 are widely used to deal with the existence of solutions for the boundary value problems of ... to the critical value c of J, that is, J u Clearly, u / since c > On the other hand, by Theorem 4.1, J has a critical point u satisfying J u supu∈Rk J u ≥ c If u / u, then Theorem 4.2 holds Otherwise, ... contradicts with 3.3 and hence the proof is complete In the existing literature, results on the nonexistence of solutions of discrete boundary value problems are scarce Hence Theorem 3.1 complements...

Ngày tải lên: 21/06/2014, 20:20

... to discuss these problems Many difficulties occur when we deal with them For example, basic tools from calculus such as Fermat’s theorem, Rolle’s theorem, and the intermediate value theorem may ... focal boundary value problems on a measure chain,” Applied Mathematics Letters, vol 18, no 1, pp 41–47, 2005 20 M Feng, X Zhang, and W Ge, “Positive solutions for a class of boundary value problems ... 1.2 , then uΔ∇ t −f t, u t ≤ 0, 3.8 which implies that u is concave on 0, T Combining this with the boundary conditions, we have uΔ > 0, uΔ < Therefore uΔ uΔ < So by 10, Theorem 1.115 , there...

Ngày tải lên: 21/06/2014, 20:20

... only if u satisfies the operator equation ∇F u 2.25 The Main Theorems Now, we state and prove the following theorem concerning the solution of problem 2.11 Theorem 3.1 Assume that there exists a ... 0, π , Rn and norm u u, u π u t , u t dt 1/2 , respectively 2.10 Boundary Value Problems Now, we consider the boundary value problem ⎧ ⎨u g t, u Au ⎩u a, t ∈ 0, π , h t , u π 2.11 b, where u ... 629–644, 2006 12 Boundary Value Problems H Wenhua, “A minimax theorem for the quasi-convex functional and the solution of the nonlinear beam equation,” Nonlinear Analysis: Theory, Methods & Applications,...

Ngày tải lên: 21/06/2014, 20:20