invariants of second order tensors
quasilinear degenerate and nonuniformly elliptic and parabolic equations of second order
... Estimates of the Gradients of Solutions of Quasilinear Elliptic Equations and Theorems of Liouville Type §1 Estimates of IVu(xo)I in terms of maxK,(xo)IuI §2 An estimate of jVu(xo)I in terms of ... local estimates of the gradients of solutions of quasilinear elliptic equations of the form (1) and their application to the proof of certain qualitative properties of solutions of these equations ... the reduction of the proof of classical solvability of problem (1.3) to the problem of constructing an a priori estimate of maxa(Iul + I Vul) for solutions of a one-parameter family of Dirichlet...
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Báo cáo hóa học: " On a class of second-order nonlinear difference equation" potx
... http://www.advancesindifferenceequations.com/content/2011/1/46 Page of and ¯ either m = ∞ or m < ∞ and xm+1 < x A negative semicycle of a solution {xn }∞ of Equation (1.1) consists of a string of n=−1 terms {xr, xr+1, , xm}, all ... lengths of positive and negative semicycles of the solution of Equation (1.1) to occur successively is , 2+, 1-, 2+, 1-, The proof for other cases, except Case 1, is completely similar to that of ... and
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Báo cáo hóa học: " Research Article Lagrangian Stability of a Class of Second-Order Periodic Systems" docx
... our proof greatly It is easy to see from the proof that this main nonlinearity is used to guarantee the small twist condition 4 Boundary Value Problems The Proof of Theorem The proof of Theorem ... curve of the Poincare mapping, which guarantees the boundedness of solutions of the system 2.11 Hence, all the solutions of 1.9 are bounded References J Littlewood, “Unbounded solutions of y ... ×S1 be a finite part of cylinder C S1 ×R, where S1 R/2πZ, we denote by Γ the class of Jordan curves in C that are homotopic to the circle r constant The subclass of Γ composed of those curves lying...
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báo cáo hóa học:" Research Article Error Bounds for Asymptotic Solutions of Second-Order Linear Difference Equations II: The First Case" pot
... of Second- order Linear Difference Equation II: the second case In the rest of this paper, we would like to give an example to show how to use the results of this paper to obtain error bounds of ... completed the estimate of the error bounds for 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 ... asymptotic solutions of second- order linear differential equations, the method used in Wong and Li’s papers cannot give us way to obtain error bounds of these asymptotic solutions Only order estimations...
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báo cáo hóa học:" Research Article Regularly Varying Solutions of Second-Order Difference Equations with Arbitrary Sign Coefficient" ppt
... positive solution z of 1.1 is normalized regularly varying, with z ∈ NRV ∪ NRV Proof First we show the last part of the statement Let {x, y} be a fundamental set of solutions of 1.1 , with y ∈ ... existence of a solution y ∈ NRV look for a solution of 1.1 in the form yk k−1 ψj j 1 j a of 1.1 Set ψk wj k ∞ j k pj − A We , 3.8 k ≥ a, with some a ∈ N In order that y is a nonoscillatory solution of ... space of sequences converging towards zero The following properties of h will play a crucial role in the proof The first two are immediate consequences of the discrete L’Hospital rule and of the...
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báo cáo hóa học:" Research Article Unbounded Solutions of Second-Order Multipoint Boundary Value Problem on the Half-Line" potx
... nonlinear second- order three-point boundary value problem,” Journal of Mathematical Analysis and Applications, vol 296, no 1, pp 265–275, 2004 Y Sun, “Positive solutions of nonlinear second- order ... problem of the second kind for a SturmLiouville operator,” Differential Equations, vol 23, pp 979–987, 1987 C P Gupta, “Solvability of a three-point nonlinear boundary value problem for a second order ... The first and second authors were supported financially by the National Natural Science Foundation of China 11071141, 10771117 and the Natural Science Foundation of Shandong Province of China Y2007A23,...
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báo cáo hóa học:" Research Article Solutions and Green’s Functions for Boundary Value Problems of Second-Order Four-Point Functional Difference Equations" ppt
... N, we denote by xt an element of Cτ defined by xt k x t k , k ∈ −τ, Boundary Value Problems In this paper, we consider the following second- order four-point BVP of a nonlinear functional difference ... ≤ s ≤ T ⎪ ⎪ ⎪ ⎩ 2.15 Proof Consider the second- order two-point BVP −Δ2 u t − f t, u u T t ∈ 1, T , 2.16 0, Boundary Value Problems It is easy to find that the solution of BVP 2.16 is given by ... ) holds Then the second- order four-point BVP 2.13 has a unique solution which is given in 2.29 Proof We need only to show the uniqueness Obviously, w t in 2.29 is a solution of BVP 2.13 Assume...
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báo cáo hóa học:" Nodal solutions of second-order two-point boundary value problems" potx
... to Lemma 2.3 Proof of main results Proof of Theorems 1.1 and 1.2 We only prove Theorem 1.1 since the proof of Theorem 1.2 is similar ν It is clear that any solution of (2.4) of the form (1, u) ... and L´pez-G´mez [7], the proofs of these o o theorems contain gaps, the original statement of Theorem 1.40 of [4] is not correct, the original statement of Theorem 1.27 of [4] is stronger than what ... existence and multiplicity of nodal solutions of the nonlinear second- order two-point boundary value problems, u + f (t, u) = 0, t ∈ (0, 1), u(0) = u(1) = The proof of our main results is based...
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báo cáo hóa học:" Research Article Oscillation of Second-Order Mixed-Nonlinear Delay Dynamic Equations" pdf
... and nonoscillation of forced second order dynamic equations,” Pacific Journal of Mathematics, vol 230, no 1, pp 59–71, 2007 12 M Bohner and S H Saker, “Oscillation of second order nonlinear dynamic ... with e t ≡ is oscillatory Proof We will just highlight the proof since it is the same as the proof of Theorem 2.6 We should remark here that taking e t ≡ and η0 in proof of Theorem 2.6, we arrive ... oscillate Some of these interval oscillation criteria were recently extended to second- order dynamic equations in 6–10 Further results on oscillatory and nonoscillatory behavior of the second order nonlinear...
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Báo cáo hóa học: " Research Article On the Spectrum of Almost Periodic Solution of Second-Order Neutral Delay Differential Equations with Piecewise Constant of Argument" ppt
... which guarantees the uniqueness of solution of 1.1 and cannot be omitted To study the spectrum of almost periodic solution of 1.1 , we firstly study the solution of 1.1 Let n s f σ dσ ds, fn n ... The proofs of Lemmas 2.2, 2.3, and 2.4 are elementary, and we omit the details Lemma 2.5 Suppose that |p| / and q / − p2 APS R , then 2.7 has a unique solution {x2n } ∈ Proof As the proof of Theorem ... {kπ : k ∈ Z} holds, where the sum of sets A and B is defined as A B {a b : a ∈ A, b ∈ B} We postpone the proof of this theorem to the next section The Proof of Main Theorem To show the Main Theorem,...
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Báo cáo hóa học: " Research Article Inequalities among Eigenvalues of Second-Order Difference Equations with General Coupled Boundary Conditions" pptx
... which proves the first conclusion ¨ The second conclusion can be shown similarly Hence, the proof is complete Finally, we turn to the proof of Theorem 3.1 Proof of Theorem 3.1 By Propositions 3.3–3.8, ... entries of the coefficient matrix of 3.6 are zero Hence, λ is a multiple eigenvalue of 1.1 and 1.2 if and only if 3.5 holds This completes the proof The following result is a direct consequence of the ... first paragraph of Section 2, ϕN−1 λ is a polynomial of degree N − in λ, ϕN λ is a polynomial of degree N − in λ, ψN−1 λ is a polynomial of degree N − in λ, and ψN λ is a polynomial of degree N in...
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Báo cáo hóa học: " Research Article Sturm-Picone Comparison Theorem of Second-Order Linear Equations on Time Scales" ppt
... equations of second order, ” Annals of Mathematics, vol 65, pp 197–202, 1957 R Zhuang, “Sturm comparison theorem of solution for second order nonlinear differential equations,” Annals of Differential ... comparison theorem of second- order differential equations see Section Remark 3.6 In the discrete case: μ t ≡ This result is the same as Sturm comparison theorem of second- order difference equations ... Scientific Foundation of Shandong Province Grant Y2007A27 , Grant Y2008A28 , the Fund of Doctoral Program Research of University of Jinan B0621 , and the Natural Science Fund Project of Jinan University...
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Báo cáo hóa học: " Research Article Global Behavior of Solutions to Two Classes of Second-Order Rational Difference Equations Sukanya Basu and Orlando Meri" docx
... completes the proof of the lemma Proof of Theorem 1.4 To prove Theorem 1.4 it is enough to assume statement B of Proposition 3.1 Also by Lemma 3.3 we may assume p / q without loss of generality ... 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 T , ... completes the proof of Theorem 1.4 Since Theorem 1.4 is just a version of Theorem 1.2 obtained by an affine change of coordinates, we have also proved Theorem 1.2 as well Proof of Theorem 1.5 The...
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Báo cáo hóa học: "Research Article Approximation of Second-Order Moment Processes from Local Averages" potx
... space of all continuous real functions on a, b M a, b denotes the space of all bounded real functions on a, b H A, a, b denotes Journal of Inequalities and Applications the space of all second order ... complex second order moment processes on a, b by some classical operators Given a probability space A, F, P , a stochastic process {X t, ω : t ∈ T, T ⊂ R} is RX t, t < ∞, said to be a second order ... study of sampling theorems For this purpose, one usually uses stochastic processes which are stationary in the wide sense as a model 8, A wide sense stationary process is only a kind of second order...
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Báo cáo hóa học: "Research Article The Shooting Method and Nonhomogeneous Multipoint BVPs of Second-Order ODE" pdf
... the study of two-point boundary value problems References [1] M K Kwong, “The shooting method and multiple solutions of two/multi-point BVPs of secondorder ODE,” Electronic Journal of Qualitative ... problem for a second order ordinary differential equation,” Journal of Mathematical Analysis and Applications, vol 168, no 2, pp 540–551, 1992 [7] C P Gupta, “A note on a second order three-point ... three-point nonlinear second order boundary value problem,” Electronic Journal of Qualitative Theory of Differential Equations, vol 2002, no 5, pp 1–11, 2002 [17] B Liu, “Positive solutions of a nonlinear...
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Báo cáo hóa học: "Research Article Solvability of Second-Order m-Point Boundary Value Problems with Impulses" docx
... constant M1 in dependent of λ ∈ [0,1] such that x ≤ M1 Furthermore, by (2.10), there is a constant M2 such that x ≤ M2 It is now immediate that the set of solutions of the family of equations (2.7) ... University References [1] C P Gupta, “Solvability of a three-point nonlinear boundary value problem for a second order ordinary differential equation,” Journal of Mathematical Analysis and Applications, ... Gupta, S K Ntouyas, and P Ch Tsamatos, “Solvability of an m-point boundary value problem for second order ordinary differential equations,” Journal of Mathematical Analysis and Applications, vol 189,...
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Báo cáo hóa học: "Research Article Nonlinear Systems of Second-Order ODEs Patricio Cerda and Pedro Ubilla" doc
... by Theorem 3.1 The proof of Theorem 5.1 is now complete Proof of main result Theorem 1.1 The proof of Theorem 1.1 is direct consequence of the following Theorem 6.1 Assume hypotheses (H1 ) through ... “Superlinear systems of second- order ODE’s,” to appear in Nonlinear Analysis: Theory, Methods ’ Applications M Conti, L Merizzi, and S Terracini, “On the existence of many solutions for a class of superlinear ... fixed points of the operator Fλ are the positive solutions of system 2.4 Lemma 4.1 The operator Fλ : X→X is compact, and the cone C is invariant under Fλ a Proof Outline The compactness of Fλ follows...
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Báo cáo hóa học: " Research Article Relations between Limit-Point and Dirichlet Properties of Second-Order Difference Operators A. Delil" pdf
... Proceedings of the Royal Society of London Series A Mathematical, Physical and Engineering Sciences, vol 380, no 1779, pp 447–486, 1982 [6] D B Hinton and R T Lewis, “Spectral analysis of second order ... Quarterly Journal of Mathematics, vol 28, no 3, pp 329–338, 1977 [8] M K Kwong, “Note on the strong limit point condition of second order differential expressions,” The Quarterly Journal of Mathematics, ... Race, “On the strong limit-point and Dirichlet properties of second order differential expressions,” Proceedings of the Royal Society of Edinburgh Section A Mathematics, vol 101, no 3-4, pp 283–296,...
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Báo cáo hóa học: " Research Article The Shooting Method and Nonhomogeneous Multipoint BVPs of Second-Order ODE" pdf
... the study of two-point boundary value problems References [1] M K Kwong, “The shooting method and multiple solutions of two/multi-point BVPs of secondorder ODE,” Electronic Journal of Qualitative ... problem for a second order ordinary differential equation,” Journal of Mathematical Analysis and Applications, vol 168, no 2, pp 540–551, 1992 [7] C P Gupta, “A note on a second order three-point ... three-point nonlinear second order boundary value problem,” Electronic Journal of Qualitative Theory of Differential Equations, vol 2002, no 5, pp 1–11, 2002 [17] B Liu, “Positive solutions of a nonlinear...
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Báo cáo hóa học: " Research Article Solvability of Second-Order m-Point Boundary Value Problems with Impulses" potx
... constant M1 in dependent of λ ∈ [0,1] such that x ≤ M1 Furthermore, by (2.10), there is a constant M2 such that x ≤ M2 It is now immediate that the set of solutions of the family of equations (2.7) ... University References [1] C P Gupta, “Solvability of a three-point nonlinear boundary value problem for a second order ordinary differential equation,” Journal of Mathematical Analysis and Applications, ... Gupta, S K Ntouyas, and P Ch Tsamatos, “Solvability of an m-point boundary value problem for second order ordinary differential equations,” Journal of Mathematical Analysis and Applications, vol 189,...
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