... equations of the motion and the boundaryconditions for the open rigid string follow from the requirement δS = ⇔ Λµ (τ, σ) = 0, (10) for the any variation δxµ obeying following conditions δxµ (τ, σ) = ... ∂xµ,1 ∂L ∂xµ,1i , (16) and the following boundaryconditions where and Cµ (τ, σ) = ∂l ∂xµ,11 (17) In the case of the closed string δµ (τ, σ) obey the conditions δµµ (τ, σ = 0) = δµ (τ, σ = σπ) ... sheet with following conditions ˙ ˙ ˙ xx′ = 0, x2 > 0, x′2 < 0, x2 = −x′2 (30) 2 2xµ = ⇔ ∂0 − ∂1 xµ (τ, σ) = (31) The functions Bµ (τ, σ), Cµ (τ, σ) which appear in boundaryconditions in the case...
... The white water filtrate is typically collected as two separate, cloudy and clear fractions In some cases, even a super clear fraction has been separated The super clear filtrate from a disk filter ... in typical European regions with difficult boundaryconditions with regard to water use All methods mentioned are therefore adapted to these specific conditions Their implementation is a success ... PAPERBREF1 is the water management concept about how to operate mills with minimum water use in European regions with difficult boundaryconditions This concept is based upon studies performed in...
... Laplacian with nonlinear boundaryconditions see [26–30], for elliptic systems with nonlinear boundaryconditions see [31, 32], for the p-Laplacian with nonlinear boundaryconditions of different ... with Dirichlet boundary value problems have been studied by Dai and Hao [24], and much weaker conditions have been given by Fan [25] The elliptic problems with nonlinear boundaryconditions have ... p(x)-Laplacian with nonlinear boundaryconditions see [38–40] Motivated by above, we focus the case of nonlocal p(x)-Laplacian problems with nonlinear Neumann boundaryconditions This is a new topics...
... Ahmad and Nieto Boundary Value Problems 2011, 2011:36 http://www.boundaryvalueproblems.com/content/2011/1/36 Page of flow phenomena, aerodynamics, fitting of experimental ... Ahmad, B, Nieto, JJ: Existence results for nonlinear boundary value problems of fractional integrodifferential equations with integral boundaryconditions Bound Value Probl 2009, 11 (2009) (Article ... equations with three-point boundaryconditions Comput Math Appl 58, 1838–1843 (2009) doi:10.1016/j.camwa.2009.07.091 Ahmad, B, Nieto, JJ: Existence of solutions for anti-periodic boundary value problems...
... with nonlinear boundaryconditions Nonlinear Anal 35, 269–286 (1999) doi:10.1016/S0362-546X(98)00034-0 15 Quintanilla, R: On the spatial blow-up and decay for some nonlinear boundaryconditions Z ... equation under nonlinear boundaryconditions In our study, we establish Phragmén-Lindelöf type theorems for equation (1.1) with nonlinear dissipative feedback terms on the boundary Our study is ... Tahamtani and Peyravi Boundary Value Problems 2011, 2011:19 http://www.boundaryvalueproblems.com/content/2011/1/19 Page of Theorem Consider the equation (1.1) subject to the conditions u(x’, 0,...
... boundary conditions, ” Boundary Value Problems, vol 2011, Article ID 720702, 20 pages, 2011 25 M Feng, D Ji, and W Ge, “Positive solutions for a class of boundary- value problem with integral boundary ... equations with integral boundary conditions, ” Boundary Value Problems, vol 2009, Article ID 708576, 11 pages, 2009 12 Z Bai, “On positive solutions of a nonlocal fractional boundary value problem,” ... anti-periodic boundary conditions, ” Nonlinear Analysis Theory, Methods & Applications, vol 69, no 10, pp 3291–3298, 2008 11 B Ahmad and J J Nieto, “Existence results for nonlinear boundary value...
... J ∈ C2 M, R , and a critical point u is called nondegenerate if the Hessian J u at this point has a bounded inverse Let u be a nondegenerate critical point of J; we call the dimension of the negative ... Equations and Applications, cı vol 11, no 2, pp 259–270, 2004 19 G M Lieberman, Boundary regularity for solutions of degenerate elliptic equations,” Nonlinear Analysis: Theory, Methods & Applications, ... number, i ≥ 2, f− x, t , f x, t denote the left and the right derivatives of f at t, respectively Boundary Value Problems f x, − α, f− x, − α for i is an even number, i ≥ For a, b ∈ R2 , f4 Let...
... then we get the boundary t−x Γ γ γ−1 ∂L dt ∂y b 3.18 Sufficient Conditions In this section, we prove the sufficient conditions that ensure the existence of a minimum maximum Some conditions of convexity ... Euler-Lagrange equations with the natural boundaryconditions Here we develop the theory of fractional variational calculus further by proving the necessary optimality conditions for more general problems ... −D α , Db− α 1, 2, 3, 2.5 Necessary Optimality Conditions 3.1 Necessary Optimality Conditions for Problem 1.1 To develop the necessary conditions for the extremum for 1.1 , assume that y∗...
... 10 Boundary Value Problems and the corresponding boundaryconditions ∂2 u ∂t2 k x ∂u k x ∂n bu ∂u ∂n 0, g u , on S1 × 0, T , 2.49 b x ≥ 0, on S2 × 0, T Acknowledgments The authors are very grateful ... dynamic boundary conditions, ” Proceedings of the Royal Society of Edinburgh Section A, vol 113, no 1-2, pp 43–60, 1989 M Kirane, “Blow-up for some equations with semilinear dynamical boundaryconditions ... dynamical boundary conditions, ” Proceedings of the London Mathematical Society, vol 93, no 2, pp 418–446, 2006 31 Z Yin, “Global existence for elliptic equations with dynamic boundary conditions, ”...
... / tj , a.e t ∈ 0, T , the limits u tj , u t− , and j Boundary Value Problems j 1, 2, , p exist, and impulsive conditions and boundaryconditions in problem 1.1 hold, we say it is a classical ... 71, no 7-8, pp 2856–2865, 2009 16 Boundary Value Problems 16 J Sun and H Chen, “Variational method to the impulsive equation with Neumann boundary conditions, ” Boundary Value Problems, vol 2009, ... 4.4 Consider boundary value problem u t λ u t − t u t −Δu tj u − u tj , uπ t / tj , a.e t ∈ 0, π , 0, j 1, 2, 4.7 Boundary Value Problems r Let σ1 √ 1/4 π, 1, it is easy to see that conditions...
... m-point boundary value problems,” Boundary Value Problems, vol 2009, Article ID 191627, 13 pages, 2009 J R Graef and J R L Webb, “Third order boundary value problems with nonlocal boundary conditions, ” ... ⎪ ⎨ v if u ≥ v ≥ 0, ⎪ v ⎪ ⎪ ⎩ u if v ≥ u ≥ b f t, v, v , 1.6 Boundary Value Problems Boundary value problems with integral boundaryconditions arise in variety of different areas of applied mathematics ... suitable conditions in this direction To the author’s knowledge, there are no necessary and sufficient conditions available in the literature for the existence of solutions for integral boundary...
... fourth-order BVPs with integral boundary conditions, one can refer to 20–24 In this paper, we are concerned with the following third-order BVP with integral boundaryconditions u t f t, u t , u ... nonlocal boundary value problem,” Discrete and Continuous Dynamical Systems Series S, vol 1, no 1, pp 89–97, 2008 20 A Boucherif, “Second-order boundary value problems with integral boundary conditions, ” ... “Second order singular boundary value problems with integral boundary conditions, ” Nonlinear Analysis: Theory, Methods & Applications, vol 72, no 5, pp 2628–2638, 2010 12 Boundary Value Problems...
... boundary conditions, ” Boundary Value Problems, vol 2009, Article ID 708576, 11 pages, 2009 A Belarbi and M Benchohra, “Existence results for nonlinear boundary- value problems with integral boundary conditions, ” ... with integral boundary conditions, ” The Rocky Mountain Journal of Mathematics, vol 40, no 1, pp 13–26, 2010 G Infante, “Nonlocal boundary value problems with two nonlinear boundary conditions, ” ... integral boundary conditions, ” Georgian Mathematical Journal, vol 1, pp 243–249, 1994 11 M Denche and A L Marhoune, “High order mixed-type differential equations with weighted integral boundary conditions, ”...
... subject to our boundaryconditions in the case n In the choice a, b 1/4, 3/4 gives the values η and μ 164 which replace our constants m and M 1/2, in the growth conditions of f The growth conditions ... involving Riemann-Stieltjes integrals The conditions 1.5 - 1.6 cover a variety of cases and include, as special cases when H2 w w, multipoint and integral boundaryconditions These are widely studied ... 2 Boundary Value Problems Multipoint versions of this problem have a physical interpretation For example, the four-point boundaryconditions u 0, u 0, u H1 u τ ,...
... nonlocal boundaryconditions if the general solution of a homogeneous equation is known Applications to Problems with NBC Let us investigate Green’s function for the problem with nonlocal boundaryconditions ... problems with nonlocal boundaryconditions NBC in this form, where i κm , u : κi , ui , m 0, 1, is a classical part and ßm , u : ßm , ui , m 0, 1, is a nonlocal m part of boundaryconditions 0, then ... with various boundaryconditions as well as additional conditions All the results of this paper can be easily generalized to the n-order difference equation with n additional functional conditions...
... remark that fractional boundaryconditions result in the existence of both electric and magnetic surface currents on the strip and are similar to the impedance boundaryconditions with pure imaginary ... integro-differential equation with fractional boundary conditions: D2 x t D1/2 x f t, x t , φx t , ψx t 0, aD1/2 x 0, < t < 1, 4.3 x η 0, < η < Acknowledgment The authors are grateful to the referees for their ... boundaryconditions and comparison with the impedance strip,” Progress In Electromagnetics Research C, vol 2, pp 189–205, 2008 13 B Ahmad and J J Nieto, “Existence of solutions for nonlocal boundary...
... 2007 Boundary Value Problems 23 R S Cantrell, C Cosner, and S Mart´nez, “Global bifurcation of solutions to diffusive logistic ı equations on bounded domains subject to nonlinear boundary conditions, ” ... purpose of this paper is to extend this study to the nonlinear boundary condition 1.5 , namely, when α x, u u u on part of the boundary Firstly, we discuss the case when n > 1, Ω Rn , n ≥ 1, ... solutions Boundary Value Problems 1, Ω Secondly, we present results for the case when n ⎧ ⎪0, ⎨ 0, , f u x u ; β > 0, and 0, ⎪ u ⎩ , x u α x, u eβu/ β 1.9 Thus, we study the nonlinear boundary...
... fractional integrodifferential equations with integral boundary conditions, ” Boundary Value Problems, vol 2009, Article ID 708576, p 11, 2009 Boundary Value Problems 19 36 J R L Webb, G Infante, ... 2010 X Zhang, X Yang, and W Ge, “Positive solutions of nth-order impulsive boundary value problems with integral boundaryconditions in Banach spaces,” Nonlinear Analysis Theory, Methods & Applications, ... value problems with integral boundaryconditions and one-dimensional p-Laplacian,” Nonlinear Analysis Theory, Methods & Applications, vol 70, no 9, pp 3119–3126, 2009 18 Boundary Value Problems 11...
... their relation with boundaryvalue problems, we refer to the book of Corduneanu 22 and Agarwal and O’Regan 23 On the other hand, boundary- value problems with integral boundaryconditions constitute ... approach, Webb et al 45 considered the widely studied boundaryconditions corresponding to clamped and hinged ends and many nonlocal boundaryconditions and established excellent existence results ... we discuss the impulsive boundary value problem with integral boundary conditions, that is, problem 1.6 includes fourth-order two-, three-, multipoint, and nonlocal boundary value problems as...