existence and uniqueness of the determinant
Báo cáo hóa học: " Research Article Global Existence and Uniqueness of Strong Solutions for the Magnetohydrodynamic Equations" potx
... 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 ... well 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 ... 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...
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Báo cáo hóa học: " Research Article Global Existence and Uniqueness of Strong Solutions for the Magnetohydrodynamic Equations Jianwen Zhang" pptx
... 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 ... well 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 ... 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...
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ON THE EXISTENCE AND UNIQUENESS OF SOLUTIONS TO BOUNDARY VALUE PROBLEMS ON TIME SCALES JOHNNY pot
... (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 ... 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 ... R on [a,σ (b)] (and there may exist further solutions satisfying y(t0 ) ≥ R for some t0 ∈ [a,σ (b)]) Proofs The proofs follow the modification technique of Theorems 3.6 and 3.7 and so are omitted...
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Báo cáo toán học: " Existence and uniqueness of nonlinear deflections of an infinite beam resting on a non-uniform nonlinear elastic foundation" pptx
... a contraction, and show the existence and the uniqueness of the solution in this space Finally, Section recapitulates the overall procedure of the article, and explains some of the intuitions ... us to use the usual argument of the Banach fixed point theorem, and to prove the existence and the uniqueness of the fixed point of Ψ, which is the solution of the differential equation (2), at ... with the physical intuition that the norm of the resulting beam deflection cannot be too large compared to that of the input loading w Meanwhile, the nonlinearity and the non-uniformity of the...
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Báo cáo hóa học: " On existence and uniqueness of positive solutions to a class of fractional boundary value problems" pot
... comparable to x and y, (5) we have the following result Theorem Adding condition (5) to the hypotheses of Theorem 1, we obtain uniqueness of the fixed point Remark In Theorems and 2, the condition ... http://www.boundaryvalueproblems.com/content/2011/1/25 Page of and they proved the existence of positive solutions by means of the Krasnosel’skii fixed-point theorem and Legget-Williams fixed-point theorem Recently, in the paper [18] to ... condition is similar to the proof of Theorem 2.3 of [23] We present this proof for completeness Theorem Under assumptions of Theorem and suppose that f(t0, 0) ≠ for certain t0 Î [0, 1] Then, Problem (2)...
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báo cáo hóa học: " On existence and uniqueness of positive solutions to a class of fractional boundary value problems" ppt
... comparable to x and y, (5) we have the following result Theorem Adding condition (5) to the hypotheses of Theorem 1, we obtain uniqueness of the fixed point Remark In Theorems and 2, the condition ... http://www.boundaryvalueproblems.com/content/2011/1/25 Page of and they proved the existence of positive solutions by means of the Krasnosel’skii fixed-point theorem and Legget-Williams fixed-point theorem Recently, in the paper [18] to ... condition is similar to the proof of Theorem 2.3 of [23] We present this proof for completeness Theorem Under assumptions of Theorem and suppose that f(t0, 0) ≠ for certain t0 Î [0, 1] Then, Problem (2)...
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Báo cáo hóa học: " Local existence and uniqueness of solutions of a degenerate parabolic system" pptx
... 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 ... 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 ... 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)...
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Báo cáo sinh học: " Research Article Existence and Uniqueness of Mild Solution for Fractional Integrodifferential Equations" docx
... 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 ... operators on a Banach space X The function a · is real valued and locally integrable on 0, ∞ , and the nonlinear maps f and g are defined on 0, T × X into X New existence and uniqueness results are given ... as a consequence of the continuity of S t in the uniform operator topology for t > by the compactness of S t So I3 → as t2 → t1 → 0, as t2 → t1 , which is independent of u Therefore Φ is Thus,...
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báo cáo hóa học:" Research Article Existence and Uniqueness of Periodic Solutions for a Class of Nonlinear Equations with p-Laplacian-Like Operators" doc
... 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 ... section, we prove an existence and uniqueness theorem for 1.1 Theorem 2.1 Suppose the following assumptions hold: A1 g ∈ C1 R, R and g x < for all x ∈ R; A2 there exist a constant r ≥ and a function ... 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...
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báo cáo hóa học:" Research Article Existence and Uniqueness of Positive Solutions for Discrete Fourth-Order Lidstone Problem with a Parameter" doc
... 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...
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báo cáo hóa học:" Research Article Existence and Uniqueness of Positive Solution for a Singular Nonlinear Second-Order m-Point Boundary Value Problem" potx
... 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...
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báo cáo hóa học:" Existence and uniqueness of nonlinear deflections of an infinite beam resting on a non-uniform nonlinear elastic foundation" docx
... a contraction, and show the existence and the uniqueness of the solution in this space Finally, Section recapitulates the overall procedure of the article, and explains some of the intuitions ... us to use the usual argument of the Banach fixed point theorem, and to prove the existence and the uniqueness of the fixed point of Ψ, which is the solution of the differential equation (2), at ... with the physical intuition that the norm of the resulting beam deflection cannot be too large compared to that of the input loading w Meanwhile, the nonlinearity and the non-uniformity of the...
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Báo cáo hóa học: "Research Article Existence and Uniqueness of Smooth Positive Solutions to a Class of Singular m-Point Boundary Value Problems" potx
... study the existence and uniqueness of smooth positive solutions to the second-order singular m-point boundary value problem 1.1 and 1.2 A necessary and sufficient condition for the existence of smooth ... Problems In view of 1.11 and the definition of Gn t, s , we can obtain u t ≥ 0, t ∈ 0, bn This completes the proof of Lemma 1.3 Now we state the main results of this paper as follows Theorem 1.4 Suppose ... Province Q2008A03 and the Doctoral Program Foundation of Education Ministry of China 200804460001 References X Du and Z Zhao, “A necessary and sufficient condition of the existence of positive solutions...
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Báo cáo hóa học: "Research Article Existence and Uniqueness of Solutions for Higher-Order Three-Point Boundary Value Problems" ppt
... of BVP 1.1 , 1.2 and satisfies 3.3 Now we give a uniqueness theorem by assuming additionally the differentiability for functions f, g and h, and a kind of estimating condition in Theorem 3.1 Theorem ... functions, and μi ∈ R, i 0, 1, , n − are arbitrary given constants The tools we mainly used are the method of upper and lower solutions and Leray-Schauder degree theory Note that for the cases of ... Proof The existence of a solution for BVP 1.1 , 1.2 satisfying 3.3 follows from Theorem 3.1 Now, we prove the uniqueness of solution for BVP 1.1 , 1.2 To this, we let x1 t x2 t − x1 t It and...
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Báo cáo hóa học: " Research Article Existence and Uniqueness of Positive and Nondecreasing Solutions for a Class of Singular Fractional Boundary Value Problems" ppt
... is comparable to x and y, 2.10 then we have the following theorem Theorem 2.9 Adding condition 2.10 to the hypotheses of Theorem 2.8 one obtains uniqueness of the fixed point of f In our considerations, ... paper we will prove the existence and uniqueness of a positive and nondecreasing solution for the problem 1.1 by using a fixed point theorem in partially ordered sets Existence of fixed point in partially ... Krasnoselskii’s fixed point theorem and nonlinear alternative of Leray-Schauder type in a cone and assuming certain hypotheses on the function f In the uniqueness of the solution is not treated...
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Báo cáo hóa học: " Research Article Existence and Uniqueness of Solutions for Singular Higher Order Continuous and Discrete Boundary Value Problems" pptx
... ∞ is continuous and nondecreasing; h : 0, ∞ → 0, ∞ is continuous and nonincreasing, and h may be singular at y Next, we consider the existence and uniqueness of solutions for the following singular ... 0, 3.5 Then from 3.4 , we have the next lemma Lemma 3.1 If x t is a solution of 3.5 , then y t is a solution of 1.1 Further, if y t is a solution of 1.1 , imply that x t is a solution of 3.5 ... Agarwal and F.-H Wong, Existence of positive solutions for higher order difference equations,” Applied Mathematics Letters, vol 10, no 5, pp 67–74, 1997 14 X Lin, D Jiang, and X Li, Existence and uniqueness...
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Báo cáo hóa học: " Research Article Existence and Uniqueness of Solutions for Singular Higher Order Continuous and Discrete Boundary " doc
... ∞ is continuous and nondecreasing; h : 0, ∞ → 0, ∞ is continuous and nonincreasing, and h may be singular at y Next, we consider the existence and uniqueness of solutions for the following singular ... 0, 3.5 Then from 3.4 , we have the next lemma Lemma 3.1 If x t is a solution of 3.5 , then y t is a solution of 1.1 Further, if y t is a solution of 1.1 , imply that x t is a solution of 3.5 ... Agarwal and F.-H Wong, Existence of positive solutions for higher order difference equations,” Applied Mathematics Letters, vol 10, no 5, pp 67–74, 1997 14 X Lin, D Jiang, and X Li, Existence and uniqueness...
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EXISTENCE AND UNIQUENESS OF SOLUTIONS OF HIGHER-ORDER ANTIPERIODIC DYNAMIC EQUATIONS ALBERTO CABADA potx
... for the existence and uniqueness of solutions of the dynamic equation (Ln ) For this, we take as reference the results obtained in [3, 4], where the existence and uniqueness of solutions of problem ... Using the results proved in Sections and 3, we will obtain in Sections and the expression of Green’s function and a sufficient condition for the existence and uniqueness of solutions of the dynamic ... obtain the following result that assures the existence and uniqueness of solutions of the dynamic equation (L1 ) in the sector [α,β], with α and β a pair of coupled lower and upper solutions of (L1...
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báo cáo hóa học:" Research Article Existence and Nonexistence of Global Solutions of the Quasilinear Parabolic Equations with Inhomogeneous Terms" pot
... 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...
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