solving systems of linear first order differential equations
Construction of the solutions of non-linear high order differential equations
... Jo _ NON-AUTONOMOUS EQUATION This p ar a g r a p h is devot ed to study of the differential equation of form (2.1) x iN) + a xx (N l) + + a N- ị i + ocNx = e F(x> X, X(N ), l$ r, ... in the first ap p roxim ation (2.14) x = £ a Jcos$J, s= and th e refinem ent o f th e first a p p r o x im a tio n ( 5) X = Yj a s COS
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Báo cáo toán học: " Minimal and maximal solutions to first-order differential equations with state-dependent deviated arguments" pptx
... solutions), unfortunately often identified in the literature on lower and upper solutions First- order differential equations with state-dependent deviated arguments have received a lot of attention in the ... compact set of fixed points in C(I), which are exactly the solutions of problem (4) Claim 2: Every solution x of (4) satisfies α ≤ x ≤ β on I and, therefore, it is a solution of (1) in [α, β] First, ... ordinary differential equations with deviated arguments J Optim Theory Appl 135(2), 257–269 (2007) Jankowski, T: Existence of solutions of boundary value problems for differential equations in which...
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báo cáo hóa học:" Research Article Limit Properties of Solutions of Singular Second-Order Differential Equations" doc
... nonlinear ordinary differential equations, ” in Handbook of Differential Equations: Ordinary a Differential Equations, A Canada, P Dr´ bek, and A Fonda, Eds., vol of Handbook of Differential ˇ Equations, ... solvability of nonlinear singular equations subject to different types of boundary conditions In this section, we utilize Theorem 4.1 to show the existence of solutions for periodic problems The rest of ... MSM6198959214 and by the Grant no A100190703 of the Grant Agency of the Academy of Sciences of the Czech Republic References J W Lee and D O’Regan, “Existence of solutions to some initial value, two-point,...
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Báo cáo toán học: " Lyapunov-type inequalities for a class of even-order differential equations" doc
... inequalities for a class of even -order differential equations Qi-Ming Zhang∗1 and Xiaofei He2 College of Science, Hunan University of Technology, Zhuzhou, Hunan 412000, P.R China College of Mathematics ... generalizations of (1.2) in some literatures Especially, Lyapunov inequality has been generalized extensively to the higher -order linear equations and the linear Hamiltonian systems A thorough ... Stability criteria for linear periodic Hamiltonian systems J Math Anal Appl 367, 329–336 (2010) [11] Wang, X: Lyapunov type inequalities for second -order half -linear differential equations J Math Anal...
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Báo cáo hóa học: " Solving systems of nonlinear matrix equations involving Lipshitzian mappings" pdf
... classes of nonlinear matrix equations (see [8-21]) In this study, we consider the following problem: Find (X1, X2, , Xm) Î (P(n))m solution to the following system of nonlinear matrix equations: ... applications to ordinary differential equations Differ Integral Equ 7, 1649–1707 (1994) Lim, Y: Solving the nonlinear matrix equation X = Q + m Mi Xδi M∗ via a contraction principle Linear Algebra Appl ... A∗ Xδi Ai = Q Linear Algebra Appl 429, 110–121 i=1 i (2008) doi:10.1016/j.laa.2008.02.014 Duan, X, Peng, Z, Duan, F: Positive defined solution of two kinds of nonlinear matrix equations Surv...
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Báo cáo hóa học: " Positive solutions of the three-point boundary value problem for fractional-order differential equations with an advanced argument" ppt
... Walter W: On some nonlinear ordinary differential equations with advanced arguments Nonlinear Anal 2003, 53:495-505 Yan JR: Oscillation of first- order impulsive differential equations with advanced ... differential equations J Math Anal Appl 2010, 371:57-68 Wang G, Ahmad B, Zhang L: Impulsive anti-periodic boundary value problem for non -linear differential equations of fractional order Nonlinear ... first order integro -differential equations with deviating arguments J Comput Appl Math 2009, 225:602-611 45 Wang G: Boundary value problems for systems of nonlinear integro -differential equations...
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báo cáo hóa học:" Research Article Nonoscillation of First-Order Dynamic Equations with Several Delays" pdf
... delay dynamic equations of first order, ” Advances in Difference Equations, vol 2008, Article ID 458687, 12 pages, 2008 10 H A Agwo, “On the oscillation of first order delay dynamic equations with ... uniqueness of solutions to systems of delay dynamic equations on time scales,” http://arxiv.org/abs/1001.0737v3 M Bohner, “Some oscillation criteria for first order delay dynamic equations, ” ... The Rocky Mountain Journal of Mathematics, vol 38, no 1, pp 1–18, 2008 11 Y Sahiner and I P Stavroulakis, “Oscillations of first order delay dynamic equations, ” Dynamic ¸ Systems and Applications,...
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báo cáo hóa học:" Research Article Homoclinic Solutions of Singular Nonautonomous Second-Order Differential Equations" doc
... solution for f having a linear behaviour near −∞ The proof is based on a full description of the set of all solutions of problem 1.1 , 1.10 for B < and on the existence of an escape solutions ... solution of problem 2.13 , 1.10 Therefore, we can borrow the arguments of 12 in the proofs of this section Theorem 3.3 If u is a damped solution of problem 1.1 , 1.10 , then u has a finite number of ... Value Problems 15 Proof Similar arugmets can be found in 12 By Lemma 2.1, the assertion i holds The arguments in Step of the proof of Lemma 4.6 imply ii The strict monotonicity of un and Remark...
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STABILITY OF PERIODIC SOLUTIONS OF FIRST-ORDER DIFFERENCE EQUATIONS LYING BETWEEN LOWER AND UPPER pptx
... optimality of the obtained results Preliminaries This paper is devoted to study the stability, by using the method of lower and upper solutions, of the N-periodic solutions of the following first -order ... see [1, 2], that the existence of α and β, a pair of lower and upper solutions of problem (PN ), such that α ≤ β in JN , does not imply the existence of a solution of this problem Alberto Cabada ... more precise description of the set of solutions of problem (PN ) Lemma 2.5 Assume conditions (H) and (H f ) Let u, v ∈ [α,β] be two solutions of problem (PN ) Then, one of the following statements...
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systems of linear inequalities (hệ bất phương trình tuyến tính) bởi a. s. solodovnikov
... Region of a System in Three Unknowns 44 Systems of Linear Inequalities in Any Number of Unknowns 52 The Solution of a System of Linear Inequalities 'by Successive Reduction of the Number of Unknowns ... inequalities is in the long run reduced to the solution of a number of systems of linear equations We shall regard the solution of a system of linear equations as something simple, as an elementary operation, ... include a remarkable analogy between the properties of linear inequalities and those of systems of linear equations (everything connected with linear equations has been studied for a long time and...
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báo cáo hóa học:" Research Article Positive Solutions to Singular and Delay Higher-Order Differential Equations on Time Scales" pptx
... existence of positive solutions The purpose of this paper is to investigate further the singular BVP for delay higherorder dynamic equation 1.1 By the use of the fixed point theorem of cone expansion ... generated by nonlinear sources, chemically reacting systems as well as concentration in chemical of biological problems Hence, two-point and multipoint boundary value problems for dynamic equations ... NSF of China 10771202 , the Research Fund for Shanghai Key Laboratory of Modern Applied Mathematics 08DZ2271900 , and the Specialized Research Fund for the Doctoral Program of Higher Education of...
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Báo cáo hóa học: " Research Article Unbounded Perturbations of Nonlinear Second-Order Difference Equations at Resonance Ruyun Ma" ppt
... Difference Equations which are real and the eigenspace corresponding to any such eigenvalue is one dimensional The following lemma is crucial to the study of nonlinear perturbations of the linear ... zero of ψ2 in [a + 1,b + 1] Then (1.6) has a solution provided b+1 h(t)ψ1 (t) = (1.11) t =a+1 The analogue of Theorem 1.4 was obtained for two-point BVPs of second -order ordinary differential equations ... pp 207–215, 2000 [7] D Bai and Y Xu, “Nontrivial solutions of boundary value problems of second -order difference equations, ” Journal of Mathematical Analysis and Applications, vol 326, no 1, pp...
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Báo cáo hóa học: " Research Article Liouville Theorems for a Class of Linear Second-Order Operators with Nonnegative Characteristic Form" potx
... one of the numerous extensions of the classical Gauss mean value theorem for harmonic functions For a proof of it, we directly refer to [6, Theorem 1.5] We would like to stress that in this proof ... independent of z0 and u, such that sup u ≤ Cu z0 (3.15) Pz0 (M) Proof It follows from Theorem 2.1 and the left translation invariance of ᏸ The details are contained in [3, Proof of Theorem 3] ... details are contained in [3, Proof of Theorem 3] From this theorem we obtain the proof of Theorem 3.1 Proof of Theorem 3.1 We may assume inf S u = Let η(s) = (γ(s),s0 − s), s0 ≤ 0, s ≥ s0 be an...
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Báo cáo hóa học: "RELIABILITY OF DIFFERENCE ANALOGUES TO PRESERVE STABILITY PROPERTIES OF STOCHASTIC VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS" pdf
... consider the stability of stochastic systems and of numerical solutions to such systems We refer the readers to a number of texts which discuss the role of stochastic systems in mathematical modelling: ... theory of stochastic differential equations type of (1.1) was studied by Gikhman and Skorokhod [10] The selected test equation (1.1) arises from the deterministic linear test equation of t ˙ Brunner ... complication of the text When considering the stability of a system we must decide on a suitable definition for stability There are a number of definitions for the stability of stochastic systems A...
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Báo cáo hóa học: "SECOND-ORDER DIFFERENTIAL EQUATIONS WITH DEVIATING ARGUMENTS" pptx
... first order differential equations of mixed type, Nonlinear [5] Analysis 64 (2006), no 9, 1984–1997 [6] D Jiang, M Fan, and A Wan, A monotone method for constructing extremal solutions to secondorder ... solutions of functional differential equations, Nonlinear Analysis 50 (2002), no 7, 885–898 [8] D Jiang, P Weng, and X Li, Periodic boundary value problems for second order differential equations ... Dynamics of Continuous, Discrete & Impulsive Systems Series A 10 (2003), no 4, 515–523 [9] V Kolmanovskii and A Myshkis, Introduction to the Theory and Applications of Functional Differential Equations, ...
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Báo cáo hóa học: " Research Article Liouville Theorems for a Class of Linear Second-Order Operators with Nonnegative " docx
... one of the numerous extensions of the classical Gauss mean value theorem for harmonic functions For a proof of it, we directly refer to [6, Theorem 1.5] We would like to stress that in this proof ... independent of z0 and u, such that sup u ≤ Cu z0 (3.15) Pz0 (M) Proof It follows from Theorem 2.1 and the left translation invariance of ᏸ The details are contained in [3, Proof of Theorem 3] ... details are contained in [3, Proof of Theorem 3] From this theorem we obtain the proof of Theorem 3.1 Proof of Theorem 3.1 We may assume inf S u = Let η(s) = (γ(s),s0 − s), s0 ≤ 0, s ≥ s0 be an...
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PERIODIC SOLUTIONS OF NONLINEAR SECOND-ORDER DIFFERENCE EQUATIONS ´ JESUS RODRIGUEZ AND DEBRA LYNN pdf
... 174 Periodic solutions of nonlinear second -order difference equations As a consequence of this result we prove that there is a countable subset S of [−2,2] such that if b∈S, then / ... to know that the columns of Ψ(·) span the solution space of the homogeneous “adjoint” problem Lx = 0, (2.14) 176 Periodic solutions of nonlinear second -order difference equations where L = XN → ... [13] Periodic solutions of nonlinear second -order difference equations J Rodriguez, An alternative method for boundary value problems with large nonlinearities, J Differential Equations 43 (1982),...
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ON THE OSCILLATION OF CERTAIN THIRD-ORDER DIFFERENCE EQUATIONS RAVI P. AGARWAL, SAID R. GRACE, AND potx
... Second Order Linear, Half -Linear, Superlinear and Sublinear Dynamic Equations, Kluwer Academic, Dordrecht, 2002 , On the oscillation of certain second order difference equations, J Differ Equations ... therein However, compared to second -order difference equations of type (1.4;δ), the study of higher -order equations, and in particular third -order equations of type (1.1;δ) has received considerably ... 346 On the oscillation of certain third -order difference equations The oscillatory behavior of second -order half -linear difference equations of the form ∆x(n) a1 (n) ∆ α1 + δq(n)...
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Báo cáo toán học: "The Central Exponent and Asymptotic Stability of Linear Differential Algebraic Equations of Index 1" pdf
... notion of the central exponent and some properties of central exponents of linear DAEs of index In Sec we investigate exponential asymptotic stability of linear DAEs with respect to small linear ... instead of X in the above formula) Now we will derive some properties of the central exponent of linear DAE of index and of its corresponding ODE Theorem 2.2 Suppose that (2.1) is a linear DAE of ... perturbed system (3.1) is a solution of some linear system of form (3.3), where F (t)x is of the same order of smallness as f (t, x), i.e δ(t), ∀t ∈ R+ F (t) (3.4) Proof From (3.2) it follows that...
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