... 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 ofthe following problem: Δu ... used the theory of semigroups in Banach spaces to give the existence and uniqueness ofthe solution for problem 1.5 – 1.7 Cavalcanti et al 7–11 studied the existence and asymptotic behavior ofsolutions ... 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 ofthe London Mathematical...
... ), then v ≥ u a.e in Ω The proof is similar to Lemma 2.2 The existence ofsolutions In this section, we introduce the main work of this paper, to prove the existence and the uniqueness ofsolutions ... 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 ofthe choice ofthe subsequence of xi Then ... ▽ = (∂1, , ∂n) is the gradient ofThe Sobolev space H1,p(Ω) is defined to be the completion ofthe set { Î C∞(Ω): ||||1,p
... Thus, the set P S defined as in (16) with α = P is nonempty and compact To complete the proof ofthe theorem, it remains to apply Theorem Existence ofSolutionsto Generalized Bilevel Vector Optimization ... from the product topology ofthe 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 ofthe words:...
... 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 ofthe LP-based algorithm employed to learn thestructureof ... 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 ofthe 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 thelinear interaction model, the abundance value of...
... Difference Equations 3.2 The Error Bound for the Asymptotic Expansion of y2 (n) Now we estimate the error bound ofthe asymptotic expansion ofthelinear independent solution y2 n tothe original ... problem of obtaining error bounds for these asymptotic solutionsto 1.2 is still open The purpose of this and the next paper Error bounds for asymptotic solutionsof second-order linear difference equations ... asymptotic solutionsto second order linear difference equations in the first case For the second case, we leave it tothe second part of this paper: Error Bound for Asymptotic Solutionsof Second-order...
... 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 ofthe lemma Now we can prove the first conjecture of ... claimed in the statement ofthe 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 ofthe two possibilities for I3 to be k-sum-free, then another computation similar tothe one in the Appendix yields that s...
... 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 oftheequations 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 ofthe article, be assumed to refer to those equations with these extra properties, though some of our...
... Aims ofthe Study The main aim ofthe thesis is to find the problems and offer solutionsto improving the English language proficiency at COT - VNU In order to achieve this aim, the thesis sets the ... from the beginning through every step ofthe way down tothe very last minutes ofthe thesis Then I would like to thank the administrators, English teachers and students at the College of Technology ... offered to test the feasibility ofthe proposed solutions ACKNOWLEDGEMENTS This study is the combination ofthe talents and contribution of all the members ofthe research groups in Pre-doctoral...
... one iron to be more loosely bound tothe enzyme than the other [34] The low occupancy ofthe proximal iron leads to an increase ofthe temperature factor of its surroundings but not to a significant ... points tothe 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 ofthe switch loop, whereby the imidazole group of His151 interacts with the bottom of F420H2 and the side chain of...
... of l-Arg leads to conversion ofthe minor population of heme centres being in the LS state into the HS state and tothe appearance of a difference spectrum [22,25–27] However, the intensity of ... series, the kcat value for the production of NO from the oxidation ofthe N-hydroxyguanidines varied by less than a factor 2, whereas the kcat value for the production of NO from the oxidation ofthe ... about the thermodynamics and kinetics ofthe binding of guanidines and N-hydroxyguanidines to iNOS Removal ofthe a-amino or a-carboxylate moiety of l-Arg has important effects on the ability of the...
... L(X , Y) the set ofthelinear 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 ofthe operator A The operator A is said to be Fredholm ... ofthe eigenvalues ofthe operator pencil with respect to its domain Let H+ be a subspace of H+ and let H be the closure ofthe set H+ in H Furthermore, let a(·, ·; λ) be the restriction ofthe ... 2.3.2 On the monotonicity ofthe eigenvalues In general, the eigenvalues λj are not monotone functions ofthe domain Ω To see this it suffices to observe the dependence ofthe eigenvalue λ2 on the angle...
... behavior ofsolutionsofthe 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 solutionsofthe 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 ofthe positive solutionsofthe system ofthe 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 solutionsofthe system of rational difference equations...
... 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 ofthe 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...
... completing the proof of Theorem 1.4 By considering the restriction ofthe map T of 1.15 to m∗ , M∗ , an application ofthe Schauder Fixed Point Theorem 17 gives that m∗ , M∗ contains the fixed point of ... solution to 5.19 converges tothe equilibrium Proof of Theorem 1.4 The four parts ofthe 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 ofthe lemma Proof of Theorem 1.4 To prove Theorem 1.4 it is enough to assume statement B of...
... 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 thelinear 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 solutionsof 1.1 are investigated using the asymptotic ... based on the asymptotic analysis ofsolutionsof 1.1 However, this approach requires the sign restriction ofthe sequence ck and additional assumptions on the convergence divergence of certain...
... conditions for the nonoscillation ofsolutionsof 1.1 Theorem 2.1 Let q t ≤ If limt → ∞ f t /|p t | nonoscillatory ∞, then all bounded solutionsof 1.1 are Proof Let y t be a bounded solution of 1.1 ... Oscillation Theory ofLinear Differential Equations, vol 48 of Mathematics in Science and Engineering, Academic Press, New York, NY, USA, 1968 23 C Tunc, “On the non-oscillation ofsolutionsof some nonlinear ... ¸ ofthe Greek Mathematical Society, vol 39, pp 131–137, 1997 26 C Tunc and E Tunc, “On the asymptotic behavior ofsolutionsof certain second-order differential ¸ ¸ equations, ” Journal of the...
... on the asymptotic behavior ofsolutionsto (1.1) Main results In this section, we study the asymptotic behavior ofsolutionstothe 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 ofsolutionsof differential equations associated to mono¸ tone operators,” Nonlinear Analysis, vol 3, no 6, pp 873–883, 1979 [4] E Mitidieri, “Asymptotic behaviour of some...
... (U), and the constant θ0 > in the condition (A) This estimate, together with the interior H¨ lder regularity ofsolutions implies the global o estimates for solutionsto problem (DP) in the H¨ ... lemmas originate from methods of Landis [13] They were essentially used in the proof ofthe interior Harnack inequality for solutionsto 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...
... (1.5) The proofs rely on the a priori bounds on solutionsof Section and the nonlinear alternative The following theorem gives the existence ofsolutionstothe Dirichlet BVP on time scales Theorem ... order to prove the existence ofsolutionstothe 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...
... 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 ofthe 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...