the structure of solutions to linear integral equations

... information In recent years, the problem has attracted a great deal of people Lions used the theory of maximal monotone operators to solve the existence of solution of the following problem: Δu ... used the theory of semigroups in Banach spaces to give the existence and uniqueness of the solution for problem 1.5 – 1.7 Cavalcanti et al 7–11 studied the existence and asymptotic behavior of solutions ... Journal of Qualitative Theory of Differential Equations, no 13, pp 1–20, 2008 30 E Vitillaro, “On the Laplace equation with non -linear dynamical boundary conditions,” Proceedings of the London Mathematical...

Ngày tải lên: 21/06/2014, 11:20

... ), then v ≥ u a.e in Ω The proof is similar to Lemma 2.2 The existence of solutions In this section, we introduce the main work of this paper, to prove the existence and the uniqueness of solutions ... sequence of X For any subsequence xij of xi, there is a subsequence xijk of, xijsuch that xijkconverges to x0 weakly in X and the weak limit x0 is independent of the choice of the subsequence of xi Then ... ▽ = (∂1, , ∂n) is the gradient of  The Sobolev space H1,p(Ω) is defined to be the completion of the set { Î C∞(Ω): ||||1,p

Ngày tải lên: 20/06/2014, 22:20

... Thus, the set P S defined as in (16) with α = P is nonempty and compact To complete the proof of the theorem, it remains to apply Theorem Existence of Solutions to Generalized Bilevel Vector Optimization ... from the product topology of the topology in Y and the weak∗ topology in Y The cone C is supposed to be nonempty, convex and closed and its polar cone have weakly∗ base B The following Theorem ... ) is said to be a solution of (1)(α,γ) The set of such solutions is said to be the solution set of (1)(α,γ) and denoted by αS2 (D, K, S, T, F, f, C) These problems (α, γ is one of the words:...

Ngày tải lên: 06/08/2014, 05:20

... Error The "Sparsity" of a graph  is the average degree of a Here, the Leave-One-Out (LOO) error is utilized to estimate the accuracy of the LP-based algorithm employed to learn the structure of ... en(t) is the abundance of gene n in profile t In most extant profiling studies, the number of transcripts monitored exceeds the number of available profiles (N Ŭ T) In the static setting, the T ... abundances of the remaining N - genes in the same profile In the dynamic setting, the T transcript profiles in E are assumed to form a time series In the linear interaction model, the abundance value of...

Ngày tải lên: 12/08/2014, 17:20

... Difference Equations 3.2 The Error Bound for the Asymptotic Expansion of y2 (n) Now we estimate the error bound of the asymptotic expansion of the linear independent solution y2 n to the original ... problem of obtaining error bounds for these asymptotic solutions to 1.2 is still open The purpose of this and the next paper Error bounds for asymptotic solutions of second-order linear difference equations ... asymptotic solutions to second order linear difference equations in the first case For the second case, we leave it to the second part of this paper: Error Bound for Asymptotic Solutions of Second-order...

Ngày tải lên: 21/06/2014, 11:20

... function of s ∈ [1, n], the cardinality of A3 attains its maximum only for some s ∈ [s − 2k, s + 2] This, together with (8), completes the proof of the lemma Now we can prove the first conjecture of ... claimed in the statement of the theorem This completes the first part of our proof (II) For the second part note that we have just shown s ≥ l3 (12) Plugging (11) into the definition of l3 yields ... s = l3 and kl3 ≥ 2r3 − 1, the latter being a requirement for either of the two possibilities for I3 to be k-sum-free, then another computation similar to the one in the Appendix yields that s...

Ngày tải lên: 07/08/2014, 08:22

... for the remainder of this argument assume that b ≥ and that 1, ∈ A The latter implies that there are no solutions in A to either of the equations x + by = c, x + by = 2c (8) (9) To continue the ... are either multiples of b in [1, z0 ] or not divisible by b This implies that |B| ≤ |An | and completes the proof of part (i) of Theorem 3.1 Proof of Part (ii) : We divide the proof into two ... homogeneous equations only For simplicity the words ‘ (linear) equation’ will, for the remainder of the article, be assumed to refer to those equations with these extra properties, though some of our...

Ngày tải lên: 07/08/2014, 15:23

... Aims of the Study The main aim of the thesis is to find the problems and offer solutions to improving the English language proficiency at COT - VNU In order to achieve this aim, the thesis sets the ... from the beginning through every step of the way down to the very last minutes of the thesis Then I would like to thank the administrators, English teachers and students at the College of Technology ... offered to test the feasibility of the proposed solutions ACKNOWLEDGEMENTS This study is the combination of the talents and contribution of all the members of the research groups in Pre-doctoral...

Ngày tải lên: 05/02/2014, 21:52

... one iron to be more loosely bound to the enzyme than the other [34] The low occupancy of the proximal iron leads to an increase of the temperature factor of its surroundings but not to a significant ... points to the di-iron center The iron closer to FMN is, in the following, referred to as proximal iron, and the other as distal iron The distance between N5 ˚ of FMN and the proximal Fe of about ... between the isoalloxazine ring of FMN and the segment between His151 and Pro153 of the switch loop, whereby the imidazole group of His151 interacts with the bottom of F420H2 and the side chain of...

Ngày tải lên: 07/03/2014, 10:20

... of l-Arg leads to conversion of the minor population of heme centres being in the LS state into the HS state and to the appearance of a difference spectrum [22,25–27] However, the intensity of ... series, the kcat value for the production of NO from the oxidation of the N-hydroxyguanidines varied by less than a factor 2, whereas the kcat value for the production of NO from the oxidation of the ... about the thermodynamics and kinetics of the binding of guanidines and N-hydroxyguanidines to iNOS Removal of the a-amino or a-carboxylate moiety of l-Arg has important effects on the ability of the...

Ngày tải lên: 16/03/2014, 22:20

... L(X , Y) the set of the linear and bounded operators from X into Y If A ∈ L(X , Y), then by ker A and R(A) we denote the kernel and the range of the operator A The operator A is said to be Fredholm ... of the eigenvalues of the operator pencil with respect to its domain Let H+ be a subspace of H+ and let H be the closure of the set H+ in H Furthermore, let a(·, ·; λ) be the restriction of the ... 2.3.2 On the monotonicity of the eigenvalues In general, the eigenvalues λj are not monotone functions of the domain Ω To see this it suffices to observe the dependence of the eigenvalue λ2 on the angle...

Ngày tải lên: 17/03/2014, 14:33

... behavior of solutions of the system of difference equations xn+1 = a + xn c + yn e + zn , yn+1 = , zn+1 = b + yn d + zn f + xn In [8], Özban studied the positive solutions of the system of rational ... rational difference equations xn+1 = yn−k , yn+1 = yn xn−m yn−m−k In [9], Zhang et al investigated the behavior of the positive solutions of the system of the difference equations xn = A + yn−p ... behavior of a three-dimensional linear fractional system of difference equations J Math Anal Appl 310, 673–689 (2005) Özban, AY: On the positive solutions of the system of rational difference equations...

Ngày tải lên: 20/06/2014, 22:20

... belongs to P and φ 0 The fractional derivative is xt θ understood here in the Caputo sense The aim of our paper is to study the solvability of 1.1 and present the existence of mild solution of 1.1 ... Difference Equations Clearly, the first term on the right-hand side of 3.20 tends to as t2 → t1 The second term on the right-hand side of 3.20 tends to as t2 → t1 as a consequence of the continuity of ... by L X the Banach space of all linear and bounded operators on X, and by C J, X the Banach space of all X-valued continuous functions on J with the uniform norm topology Let us recall the definition...

Ngày tải lên: 21/06/2014, 05:20

... completing the proof of Theorem 1.4 By considering the restriction of the map T of 1.15 to m∗ , M∗ , an application of the Schauder Fixed Point Theorem 17 gives that m∗ , M∗ contains the fixed point of ... solution to 5.19 converges to the equilibrium Proof of Theorem 1.4 The four parts of the proof are as follows a f x, y is increasing in both x and y on m∗ , M∗ By Lemma 5.2 the hypotheses of Theorem ... asymptotically stable equilibrium for 4.33 by Lemma 4.4, it follows that yn → u This completes the proof of the lemma Proof of Theorem 1.4 To prove Theorem 1.4 it is enough to assume statement B of...

Ngày tải lên: 21/06/2014, 20:20

... distinguished solution of 2.1 , then the associated solution of 1.1 given by the formula k−1 Φ−1 xk j m wj rj is said to be the recessive solution of 1.1 , see Note that in the linear case p x of 1.2 is ... At the end of this section, for the sake of comparison, we recall the main results of 8, 17 , where summation characterizations of recessive solutions of 1.1 are investigated using the asymptotic ... based on the asymptotic analysis of solutions of 1.1 However, this approach requires the sign restriction of the sequence ck and additional assumptions on the convergence divergence of certain...

Ngày tải lên: 21/06/2014, 20:20

... conditions for the nonoscillation of solutions of 1.1 Theorem 2.1 Let q t ≤ If limt → ∞ f t /|p t | nonoscillatory ∞, then all bounded solutions of 1.1 are Proof Let y t be a bounded solution of 1.1 ... Oscillation Theory of Linear Differential Equations, vol 48 of Mathematics in Science and Engineering, Academic Press, New York, NY, USA, 1968 23 C Tunc, “On the non-oscillation of solutions of some nonlinear ... ¸ of the Greek Mathematical Society, vol 39, pp 131–137, 1997 26 C Tunc and E Tunc, “On the asymptotic behavior of solutions of certain second-order differential ¸ ¸ equations, ” Journal of the...

Ngày tải lên: 22/06/2014, 02:20

... on the asymptotic behavior of solutions to (1.1) Main results In this section, we study the asymptotic behavior of solutions to the evolution equation (1.1) under appropriate assumptions on the ... prove the strong convergence of u by assuming A to be strongly monotone Theorem 2.6 Assume that the operator A is strongly monotone, and let u be a solution to (1.1) Then u(t) converges strongly to ... “Asymptotic behaviour of solutions of differential equations associated to mono¸ tone operators,” Nonlinear Analysis, vol 3, no 6, pp 873–883, 1979 [4] E Mitidieri, “Asymptotic behaviour of some...

Ngày tải lên: 22/06/2014, 18:20

... (U), and the constant θ0 > in the condition (A) This estimate, together with the interior H¨ lder regularity of solutions implies the global o estimates for solutions to problem (DP) in the H¨ ... lemmas originate from methods of Landis [13] They were essentially used in the proof of the interior Harnack inequality for solutions to elliptic and parabolic equations in the non-divergence form ... for operators L in the form (ND) and the boundary ∂Ω of class C (see [10]) In Theorem 3.9, we extend this result to domains Ω satisfying an exterior sphere condition The proof of this theorem...

Ngày tải lên: 22/06/2014, 22:20

... (1.5) The proofs rely on the a priori bounds on solutions of Section and the nonlinear alternative The following theorem gives the existence of solutions to the Dirichlet BVP on time scales Theorem ... order to prove the existence of solutions to the BVPs (1.1), (1.2) through (1.1), (1.5), the following theorem will be used, which is referred to as the nonlinear alternative of Leray-Schauder Theorem ... operator by the Arzela-Ascoli theorem Therefore, Theorem 1.8 is applicable to T and T must have a fixed point Hence the BVP has a solution This concludes the proof The following theorem gives the...

Ngày tải lên: 23/06/2014, 00:20

... have the conclusion that the sequence (3.10) {u m } m converges to u in X k Thus, Tk is of class ( S )+ in X k Next we calculate the topological degree of the operator Tk By condition (C4), the ... Topological degree for a class of operators and applications, Nonlinear Analysis 57, 505-518, (2004) [5] M.A Krasnosel´kii, Topological methods in the theory of nonlinear integral equations, Pergamon Press, ... X* , t ∈ [ 0,1] be the homotopy family of operators of class ( S )+ Suppose that A t u ≠ for u ∈ ∂D, t ∈ [ 0,1] Then deg ( A , D, ) = deg ( A1 , D, ) NONLINEAR ELLIPTIC EQUATIONS WITH UNBOUNDED...

Ngày tải lên: 22/07/2014, 10:21