the first boundary value problem for quasilinear nonuniformly parabolic equations
báo cáo hóa học: " On the solvability conditions of the first boundary value problem for a system of elliptic equations that strongly degenerate at a point" pdf
... article as: Rutkauskas: On the solvability conditions of the first boundary value problem for a system of elliptic equations that strongly degenerate at a point Boundary Value Problems 2011 2011:16 ... due to the definition of matrix Q(k) Hence, there holds the following n Rutkauskas Boundary Value Problems 2011, 2011:16 http://www.boundaryvalueproblems.com/content/2011/1/16 Page of 11 Theorem ... in the opposite case The uniqueness of the solutions of both the problems D1 and D2 yields the following lemma Lemma Let v = (v1, v2, , vs) be a solution of problem D1 or problem D2 with the...
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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
... G: Integral boundary value problems for first order integro-differential equations with deviating arguments J Comput Appl Math 2009, 225:602-611 45 Wang G: Boundary value problems for systems ... p-Laplacian boundary value problems with advanced arguments Appl Math Comput 2009, 215:125-131 Jankowski T: Solvability of three point boundary value problems for second order differential equations with ... three point boundary value problems via fixed point index theory Nonlinear Anal 2001, 47:4319-4332 Raffoul YN: Positive solutions of three-point nonlinear second order boundary value problem Electron...
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ON A BOUNDARY VALUE PROBLEM FOR NONLINEAR FUNCTIONAL DIFFERENTIAL EQUATIONS ROBERT HAKL Received 21 doc
... multi-point boundary value problems for systems of functionaldifferential and difference equations, Mem Differential Equations Math Phys (1995), 1– 113, 133 R Hakl, On some boundary value problems for systems ... no 2, 184–193 , On the solvability of nonlinear boundary value problems for functional-differential equations, Georgian Math J (1998), no 3, 251–262 , Boundary Value Problems for Systems of Linear ... 25, 28, 29, 30, 31, 32, 37, 40, 42] and the references therein) In spite of this, the general theory of boundary value problems for functional differential equations is not still complete Here,...
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Báo cáo toán học: "On the Smoothness of Solutions of the First Initial Boundary Value Problem for Schr¨dinger o Systems in Domains with Conical Points" pps
... we find that eigenvalues of the problem (2.24) are ikπ π λk = ± , k ∈ N∗ Therefore, if β < then the strip ≤ Imλ ≤ + l β l+1 does not contain eigenvalues of the problem (2.24) By Theorem 2.2, we ... Anh, On the solvability of the first initial boundary value problem for Schr¨dinger systems in infinite cylinders, Vietnam J Math 32 o (2004) 41– 48 V A Kondratiev, Boundary value problems for elliptic ... ∂ k apq q D ∂tk By Theorem 2.1 the function v = uts still satisfies the boundary conditions Therefore from inductive hypothesis and by repeating arguments of the proof in the case s = 0, we obtain...
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báo cáo hóa học: " On the regularity of the solution for the second initial boundary value problem for hyperbolic systems in domains with conical points" pptx
... (2:5) holds for all u, v ∈ C∞ ( ) and for all t Î [0, ∞) The order of the operator Nj is 2m j for j = 1, 2, , m Hung et al Boundary Value Problems 2011, 2011:17 http://www.boundaryvalueproblems.com/content/2011/1/17 ... \{0}) for a.e t Î (0, ∞), and therefore, (4.19) holds for h - Now we prove the assertion of the theorem by induction on h Let us consider first the case h = We rewrite (2.6), (2.7) in the form ... (3:20) Hung et al Boundary Value Problems 2011, 2011:17 http://www.boundaryvalueproblems.com/content/2011/1/17 Page of 18 From these equalities together with the initial (3.6) and the assumption...
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báo cáo hóa học: " An initial-boundary value problem for the one-dimensional non-classical heat equation in a slab" potx
... and the thesis holds.▀ Another related problem Now, we will consider a new non-classical initial -boundary value problem (P5) for the heat equation in the slab [0,1], which is related to the previous ... generalization of the moving boundary problem for the classical heat equation [13] which can be useful in the study of free boundary problems for the heat-diffusion equation [12] We will use the Neumann ... extended to the interval ≤ t ≤ T Salva et al Boundary Value Problems 2011, 2011:4 http://www.boundaryvalueproblems.com/content/2011/1/4 Page 10 of 17 Proof It is similar to the one given for Theorem...
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báo cáo hóa học:" Research Article Nonlocal Four-Point Boundary Value Problem for the Singularly Perturbed Semilinear " pot
... are formed due to the nonuniform convergence of the exact solution y to the solution u of a reduced problem in the neighborhood of the ends a and b of the bar The differential equations of the form ... contrast to the “standard” boundary conditions as the Dirichlet problem, Neumann problem, Robin problem, periodic boundary value problem 9–12 , for example In the problem considered; there is not ... of the √ We will write s O r when < lim → |s /r | < ∞ order O The situation in the case of nonlocal boundary value problem is complicated by the fact that there are the inner points in the boundary...
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Báo cáo hóa học: " Research Article Nonlinear Boundary Value Problem for Concave Capillary Surfaces Occurring in Single Crystal Rod Growth from the Mel" ppt
... priori The state of the arts at the time 1993-1994, concerning the dependence of the shape and size of the free surface of the meniscus on the pressure difference p across the free surface for small ... minimum of the free energy of the melt column For the growth of a single crystal rod of radius r1 ; < r1 < r0 , the differential equation for axisymmetric meniscus surface is given by the formula ... that the lower edge of the free surface is fixed to the outer edge of the shaper The growth angle αg and the contact angle αc , which appear in the above relations, are material constants and for...
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The greens function for the initial boundary value problem of one dimensional navier stokes equation
... modern mathematics In this thesis, We will focus on the one dimensional Navier-Stokes equations and consider the initial -boundary value problem There are a lot of works on the initial value problems ... than the initial value problem However, so far there is not much knowledge on the initial -boundary value problem due to it’s mathematical difficulty Our goal is to study the Navier-Stokes equations ... to build the relationship between the solutions of initial value problem and initial -boundary value problem The Laplace transformation is frequently used to solve kinds of initial value problems...
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Báo cáo hóa học: " Research Article Existence of Positive Solutions to a Boundary Value Problem for a Delayed Nonlinear Fractional Differential System " ppt
... contraction Therefore, the proof is complete with the help of Lemmas 3.1 and 2.5 The following result can be proved in the same spirit as that for Theorem 3.4 8 Boundary Value Problems Theorem 3.5 For ... 2 Boundary Value Problems study on systems of fractional differential equations, not much has been done for boundary value problems for systems of fractional differential equations 18–20 On the ... t, s > for < s ≤ t < Therefore, Gi t, s > for < s ≤ t < and the proof is complete Lemma 3.3 (i) If ni 2, then Gi t, s ≤ Gi s, s for t, s ∈ 0, × 0, (ii) If ni > 2, then Gi t, s < Gi 1, s for t,...
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Báo cáo hóa học: " Research Article Existence of Solutions to Anti-Periodic Boundary Value Problem for Nonlinear Fractional " potx
... years For the general theory of impulsive differential equations, we refer the reader to 7, Recently, many authors are devoted to the study of boundary value problems for impulsive differential equations ... Luo, “Multiple positive solutions of the singular boundary value problem for second-order impulsive differential equations on the half-line,” Boundary Value Problems, vol 2010, Article ID 281908, ... a solution of the problem 1.1 In the following theorem we give an existence result for the problem 1.1 by applying the nonlinear alternative of Leray-Schauder type and by which the conditions...
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Báo cáo hóa học: " Research Article Nonlocal Boundary Value Problem for Impulsive Differential Equations of Fractional Order" ppt
... play an important role in theory and applications, see the references 15–21 and references therein However, as pointed out in 15, 16 , the theory of boundary value problems for nonlinear impulsive ... four-point nonlocal boundary value problem of nonlinear integrodifferential equations of fractional order by applying some fixed point theorems On the other hand, impulsive differential equations of fractional ... fractional differential equations is still in the initial stages Ahmad and Sivasundaram 15, 16 studied the following impulsive hybrid boundary value problems for fractional differential equations, respectively,...
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Báo cáo hóa học: " Research Article Positive Solution of Singular Boundary Value Problem for a Nonlinear Fractional Differential Equation" potx
... |, 3.10 G t, s ds < 1, the boundary value problem 1.2 has a unique positive Proof According to Theorem 3.1, if the conditions in Theorem 3.1 hold, then the boundary value problems 1.2 have at least ... ds < 1, the operator T is the contraction mapping Then by Banach contraction fixed-point theorem, the boundary value problem 1.2 has a unique positive solution u t ∈ S Boundary Value Problems ... solution to this problem by a fixed-point theorem in partially ordered sets Other related results on the boundary value problem of the fractional differential equations can be found in the papers 11–23...
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báo cáo hóa học:" Research Article A Mixed Problem for Quasilinear Impulsive Hyperbolic Equations with Non Stationary Boundary and Transmission Conditions" ppt
... t is the solution of problem 1.1 - 1.2 , then w t is the solution of the problem 1.16 On the contrary, if w t ∈ C2 0, T ; H ∩ C1 0, T ; H1 , H 1/2 ∩ C 0, T ; H1 1.18 is the solution of problem ... Difference Equations Abstract Model of Initial Boundary Value Problem with Non Stationary Boundary and Transmission Conditions for the Impulsive Semilinear Hyperbolic Equations Consider the following ... 2.10 Advances in Difference Equations 11 Thus, the nonlinear operator F satisfies the condition of local solvability of the Cauchy problem for the quasilinear hyperbolic equations in Hilbert space...
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báo cáo hóa học:" Research Article Existence and Multiplicity of Positive Solutions of a Boundary-Value Problem for Sixth-Order ODE with Three Parameters" pdf
... get the 2L-stationary spatial periodic solutions of 1.2 , one turns to study the two points boundary- value problem 1.1 The 2L-periodic extension u of the odd extension of the solution u of problems ... variational method and linking theorems On the other hand, The positive solutions of fourth-order boundary value problems 1.5 have been studied extensively by using the fixed point theorem of cone extension ... false The proof is completed 2.7 Boundary Value Problems Let Gi t, s i 1, 2, be Green’s function of the linear boundary- value problem −u t Lemma 2.3 see Gi t, s i λi u t 0, u u 2.8 1, 2, has the...
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báo cáo hóa học:" Positive solutions for boundary value problem for fractional differential equation with $p$-Laplacian operator" doc
... Guo-Krasnosel’ski˘ ı’s fixed point theorem, Zhao et al investigated the existence of positive solutions for the nonlinear fractional boundary value problem (BVP for short) α D u(t) = λf (u(t)), ... u(ξ2 ) On the other hand, integer-order p-Laplacian boundary value problems have been widely studied owing to its importance in theory and application of mathematics and physics, see for example, ... and the references therein Especially, in [29], by using the fixed point index method, Yang and Yan investigated the existence of positive solution for the third-order Sturm–Liouville boundary value...
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Báo cáo hoa học: "Research Article Solutions of 2nth-Order Boundary Value Problem for Difference Equation via Variational Method" pot
... functional for BVP 1.1 - 1.2 is constructed which transforms the existence of solutions of the boundary value problem BVP to the existence of critical points of this functional In order to prove the ... all eigenvalues of BT B are real and positive Let λ be the minimal eigenvalue of these N eigenvalues, then λ > Therefore xT BT Bx λxT x, that is, N Δn xk λ x 1−n However, how to find the λ in ... to the the fact that {φ y m } is bounded pλ − r2 /2 > Next we use the mountain-pass lemma to finish the proof By i , for r2 R1 Then 0, there exists R1 > such that f k, y /y for |y| /2 y2 for...
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Báo cáo hóa học: " Research Article On a Mixed Nonlinear One Point Boundary Value Problem for an Integrodifferential Equation" pdf
... Ladyzhenskaya, The Boundary Value Problems of Mathematical Physics, vol 49 of Applied Mathematical Sciences, Springer, New York, NY, USA, 1985 L Garding, Cauchy Problem for Hyperbolic Equations, Lecture ... ⊂ L2 QT By the Schauder σ σ σ σ fixed point theorem the mapping h has a fixed point u in W C, D Remark 3.4 For compactness of the set W C, D , see also 8, Remark 3.5 The following theorem gives ... regularity result for the solution of 2.1 – 2.3 More precisely, one should expect the solution 2,1 to be in Wσ,p QT with p ≤ ∞ Theorem 3.6 Let u ∈ Vσ be a solution of problem 2.1 – 2.3 , then the following...
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Báo cáo hóa học: "Research Article A Boundary Value Problem for Hermitian Monogenic Functions" doc
... Γ, the last equality being a consequence of the Painlev´ and Liouville theorems e We thus arrive to another characterization for the solvability of the jump problem 1.11 Theorem 3.2 The jump problem ... continuity, we get ν|ν ∂ω g ∂ω| g 3.6 Boundary Value Problems On the other hand, if g satisfies 3.6 , then for G G ν|∂ν F ∂ x| F, ∂x| F, we have ν ∂ν F ∂ x F 3.7 Therefore in a neighbourhood of Γ intersected ... by the results obtained in 9, 10 where a similar problem was studied for two-sided monogenic functions For the case of harmonic vector fields, we refer the reader to 11 In order to solve problem...
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ON A PERIODIC BOUNDARY VALUE PROBLEM FOR SECOND-ORDER LINEAR FUNCTIONAL DIFFERENTIAL EQUATIONS S. pptx
... homogeneous problem v (t) = (v)(t) (i) for ≤ t ≤ ω, (i) v (0) = v (ω) (i = 0,1) (4.1) (4.2) It is known from the general theory of boundary value problems for functional differential equations that ... operator, then problem (1.1), (1.2) has the Fredholm property (see [3, Theorem 1.1, page 345]) Thus, the problem (1.1), (1.2) is uniquely solvable iff the homogeneous problem (4.1), (4.2) has only the ... As for the case where p(t) ≥ for ≤ t ≤ ω, the necessary and sufficient condition for the unique solvability of (2.19), (1.2) is p(t) ≡ (see [2, Proposition 1.1, page 72]) 252 On a periodic BVP for...
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