existence and uniqueness of the solution

... we prove the uniqueness of the equation when the conditionH1 and H2 holds Let x1t and x2t be two 2π-periodic solutions of the problem Denote x0t  x1t − x2t, t ∈ 0, 2π, then x0t ... obtained by combining the classical method of lower and upper solutions and the method of alternative problemsThe Lyapunov-Schmidt method as discussed by many authors 1 10 In 11, the author gives ... for t ∈ ξ1, ξ2 Also xξ1  0 Therefore, xt ≡ 0 for t ∈ 0, 2π, a contradiction The proof is complete Firstly, we prove the existence of the solution Consider the homotopy equation x αx

Ngày tải lên: 14/07/2023, 09:44

... ensure that the fuzzy solutions exist without unique-anycondition on data and the boundary of the domain New weighted metrics are used Trang 3The existence and uniqueness of fuzzy solutionsand suitable ... chosen in order to prove that the existence anduniqueness of fuzzy solutions only depend on the Lipschitz property of the right side of the equations Moreover, the problems with fuzzy integral ... holds Then the problem (1)–(2) has a unique solution in C(J a × J b , E n ). Trang 7The existence and uniqueness of fuzzy solutionsProof From Definition3.2, we realize that fuzzy solution of problem

Ngày tải lên: 16/12/2017, 08:45

... definitions and lemmas In Section 3, by using the method of coincidence degree theory, we obtain the existence of the anti-periodic solutions of system 1.1 In Section 4, we give the criteria of global ... anti-periodic solutions to neural networks with impulse The main purpose of this paper is to study the existence and global exponential stability of anti-periodic solutions of system 1.1 by using the method ... Using the time scales calculus theory, the coincidence degree theory, and the Lyapunov functional method, we obtain sufficient conditions for the existence and global exponential stability of anti-periodic

Ngày tải lên: 21/06/2014, 07:20

... Turkey Full list of author information is available at the end of the article Abstract In this manuscript, by using the fixed point theorems, the existence and the uniqueness of solutions for multi-term ... point theorem; multi-term nonlinear fractional differential equation Introduction The study of fractional differential equations ranges from the theoretical aspects of existence and uniqueness of solutions ... u() = , where  < α ≤ ,  < β ≤ , and f is continuous on [, ] × R × R [] In , Su and Zhang studied the existence and uniqueness of solutions for the following nonlinear two-point fractional

Ngày tải lên: 02/11/2022, 10:38

... cheese, and, on the other hand, to establish the influence of the smoking process on the volatile profile of this type of cheese This will contribute to define the aromatic profile of this type of ... means of SPME followed by GC/MS for the subsequent study of the extracted compounds The purpose of this work is, on the one hand, to characterize the components of the headspace of unsmoked and ... derivatives and ethers detected in the headspace of the exterior region of unsmoked (U) and smoked (A and B) Herreño cheeses studied, together with their molecular weight, the base peak of their mass

Ngày tải lên: 19/11/2022, 11:42

... that the functions ˆb and ˆσ satisfy the locally Lipschitz and H¨older continuity and the lineargrowth over the set R × Rd with the same constants L1 and K1 defined in H1 For the rest of the paper ... ,where X is the solution to the stochastic differential equation where c0, K1, K2, K3 and k are the constants defined in H1 and H2 The proof of this Theorem will be a consequence of several results ... process and second,the continuity of the flow process does not imply the continuity with respect to t Because of these, we consider Trang 5the augmented process (ξ(s), X(s)) defined as the solution

Ngày tải lên: 24/11/2022, 17:57

... is not The assumption in Theorem 2.1 we have imposed in this Theorem 4.1 of [8] and [7]) Example 2.4 shows that the lower semicontinuity of K2 needs to be added to Theorem 4.1 of [8] and [7] ... µ) are the solution sets of (QEP λ γµ ) and (QEEP λ γµ ), respectively A α and let and Ξα ( λ , γ , µ ) α Throughout the paper we assume that Σ ( λ , γ , µ ) ≠∅ α and each ( λ , γ , µ in the ( ... ) The further argument is the same as above And so we have Ξ m is closed at (λ , γ , µ0 ) □ Remark 2.9 Theorem 2.8 is an extension of Theorem 4.1 in [8] The Example 2.3 is also shows that the

Ngày tải lên: 05/01/2023, 13:29

... outside the spectral region shown. Trang 4the a-helices on one side of the b-sheet and two on theother side The rmsd of the heavy atoms (Ca, C, and N) of the protein core, when the NMR structures of ... between the HN of Thr358 and the Ha of His356 could be seen in both conformers (Fig 4; Fig S3) At the same time, the intensity of the NOE between the HN of Phe357 and the Ha of Lys354 in the open conformer ... in the open conformer, and partially by faster exchange of the amide proton of Gly337 with water The second A Fig 3 The solution structure of the C-domain (A) Stereo view of the ensemble of the

Ngày tải lên: 06/03/2014, 11:20

... b-strands 3 and 4 The b-strands 2 (residues Ile30–Phe31) and 5 (residues Val48–Lys49)form the second b-sheet The Fig 4 Identification of the IsoAsp66–Gly67 connectivity (A)The deamidation of the ... to other proteins of this class, such as the DNA-binding domain of the Mu repressor [21] Third, the backbone atoms of the region comprising the
wing b-sheet (residues 2–4, 35–36 and 41–44 of ... to excision of the prophage by recombination between attR and attL and regeneration of the attP and attB sites The excision requires an additional enzyme – the excisionase (Xis) The cellular

Ngày tải lên: 23/03/2014, 15:21

... stabi- lizes the positive charges of the adjacent Lys9 and Lys39. Similarly, Asp23 stabilizes the juxtaposed Lys15 and Lys17 side chains. The hydrophobic strand b4 is located between Cys43 and Asp46 and, ... with their phenolato side chains can be found closely positioned in the space between b4 and loop 2 and create a well- defined aromatic region of the protein. The topology of the disulfide pairs and ... 10. The electrostatic surface potential of AFP (left) and PAF (right) structures representing the orientation of the side chain lysine resi- dues. Lys9, Lys35 and Lys38 of PAF and Lys9, Lys32 and

Ngày tải lên: 29/03/2014, 23:20

... in the proof of the uniqueness of strong solutions Global existence of strong solutions In this section, we prove the global existence of strong solutions to the problem 1.2 – 1.7 by applying the ... This completes the proof of Theorem 1.1 except the uniqueness assertion because of the presence of vacuum , which will be proved in the next section Uniqueness and stability of strong solutions In ... 1.7 mean that the boundary is nonslip and impermeable The purpose of the present paper is to study the global existence and uniqueness of strong solutions of problem 1.2 – 1.7 The important...

Ngày tải lên: 22/06/2014, 06:20

... theorem, we have the conclusion of the theorem Remark 3.3 In Theorem 3.2, if we furthermore suppose that the hypothesis H4 − f t, v t f t, u t ≤L u−v , L > 0, 3.28 holds, then we can obtain the ... especially the estimating approaches given in 4, 6, 10, 24, 27 , we investigate the existence and uniqueness of mild solution of 1.1 in a Banach space X: −A generates a compact semigroup S · of uniformly ... the uniqueness of the mild solution in Theorem 3.2 Actually, from what we have just proved, 1.1 has a mild solution u t and t u t Q t u0 R t − s f s, u s 3.29 K u s ds Let v t be another mild solution...

Ngày tải lên: 21/06/2014, 16:20

... suggestions and comments, which improved the quality of this paper The work was supported by the NSF of China, the NSF of Jiangxi Province of China 2008GQS0057 , the Youth Foundation of Jiangxi ... special case and its variants, where ϕp s of 1.1 However, there are seldom results about the existence of periodic solutions to 1.1 The main difficulty lies in the p-Laplacian-like operator ϕ of 1.1 ... ϕp s , Liu 7, Theorem proved that 1.1 has a unique T -periodic solution ϕp s , Theorem 2.1 under the assumptions A1 and A2 Thus, even for the case of ϕ s is a generalization of 7, Theorem In...

Ngày tải lên: 21/06/2014, 18:20

... solution of the BVP 1.1 and 1.2 Next, we show the uniqueness of solutions of the BVP 1.1 and 1.2 Assume, to the contrary, that there exist two nontrivial solutions y1 and y2 of the BVP 1.1 and 1.2 ... relax the assumptions A1 and B1 on the nonlinear term, without demanding the existence of upper and lower solutions, we present conditions for the BVP 1.1 and 1.2 to have a unique solution and then ... 1–7 and references therein Especially, there was much attention focused on the existence and multiplicity of positive solutions of fourth-order problem, for example, 8–10 , and in particular the...

Ngày tải lên: 21/06/2014, 18:20

... completes the proof of the theorem Boundary Value Problems 13 Theorem 3.2 Assume that conditions C0 , C1 , and C2 are satisfied Then SBVP 1.1 , 1.2 has exactly one positive solution Proof The uniqueness ... completes the proof of the lemma Lemma 2.7 Assume that conditions C0 , C1 , and C2 are satisfied Then, the unique solution u t; h of BVP 2.1 h is nondecreasing in h Proof Let < h2 < h1 , and let ... s ds Take t ∈ 0, and Δt such that t Δt ∈ 0, , then from the definition of derivative, the mean value theorem of Boundary Value Problems integral, and the absolute continuity of integral, we have...

Ngày tải lên: 21/06/2014, 18:20

... 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 existence ... Proofs The proofs follow the modification technique of Theorems 3.6 and 3.7 and so are omitted for brevity On nonincreasing solutions Some results about the qualitative nature of solutions for the ... satisfy y < R and are solutions to the BVP (1.12), (1.3) This concludes the proof Theorem 3.8 Let the conditions of Theorem 3.3 hold with (2.1) replaced by (3.23) and C /α < R Then the BVP (1.12),...

Ngày tải lên: 23/06/2014, 00:20

... QT , u1 , u2 ∈ R Existence and uniqueness In this section, we show the local existence and uniqueness of weak solutions of (1.1)(1.3) First, we show the local existence results Theorem 2.1 Assume ... u2) is a weak solution of (1.1)(1.3) □ The following is the uniqueness result to the solution of the system Theorem 2.2 Assume that f = (f1, f2) is Lipschitz continuous in (u1, u2), then (1.1)(1.3) ... carried out the proof of existence, BW conceived of the study, and participated in its design and coordination All authors read and approved the final manuscript Competing interests The authors...

Ngày tải lên: 21/06/2014, 03:20

... results as Theorem in are obtained in We will prove Theorem 1.1 a and b in Sections and 4, respectively The proof of Theorem 1.2 is included in the proof of Theorem 1.1 a In the following, R and T ... > 0, and p > max{1, m} Then every nontrivial solution u x, t of 1.1 blows up in finite time Remark 1.3 Theorems 1.1 and 1.2 are the extension of the results of If we put σ these theorems, the ... the other hand, 6–9 and so on study the inhomogeneous equations i.e., f x / ≡ in 1.1 Bandle et al study the case m 1, σ 0, and Zeng and Zhang study the case σ In this paper, we investigate the...

Ngày tải lên: 21/06/2014, 11:20