... Lagrangian , and the fact that the field xµ (τ, σ) is defined on the finite strip σ π , and −∞ < τ < ∞, which has boundaries The classical equations of the motion and the boundaryconditions for ... ∂L + ∂i ∂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, ... = const (18) ∂L ∂xµ = and δS = with the conditions xµ (τ, σ) obeys Assume the Lagrangian is invariant, the equations of motion (13), andconditions (14) and (15) From (9) we have π Pµ = dσ − ∂L...
... equationsand 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 ... approach, Webb et al 45 considered the widely studied boundaryconditions corresponding to clamped and hinged ends and many nonlocal boundaryconditionsand established excellent existence results for ... , 0, ∞ and may be singular at t or t 1; f, g : 0, × P \ {θ} × 0; , bi , ci , and P \ {θ} → P are continuous and may be singular at t 0, 1, u 0, and u di ∈ 0, ∞ , and ρi ci di bi ci > 0, and mi...
... sandy as a result of high fluvial sediment input during flood periods which nourish the mainland beaches and sandy barriers that form across estuary mouths and tidal inlets Mainland beaches and ... with a radial loader and coal is unloaded with a pneumatic unloader Boundaryconditions To get insight in the environmental boundary conditions, field data is collected and analysed thoroughly ... loading and unloading capacity should be available The hinterland connections should be efficient and have enough capacity In Paragraph 1.1.2 it was stated that knowledge and understanding about...
... type equations 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 ... nonlinear boundaryconditions see [26–30], for elliptic systems with nonlinear boundaryconditions see [31, 32], for the p-Laplacian with nonlinear boundaryconditions of different type see [33–37], and ... Existence and multiplicity of solutions for nonlocal p(x)-Laplacian equations with nonlinear Neumann boundaryconditions Erlin Guo∗ and Peihao Zhao School of Mathematics and Statistics,...
... Theory andApplications of Fractional Differential Equations In North-Holland Mathematics Studies, vol 204,Elsevier, Amsterdam (2006) 21 Samko, SG, Kilbas, AA, Marichev, OI: Fractional Integrals and ... fractional integro-differential equations with fractional nonlocal integral boundaryconditionsBoundary Value Problems 2011 2011:36 Submit your manuscript to a journal and benefit from: Convenient ... sup(t,x,φx,ψx)∈[0,T]×Br ×Br ×Br |f (t, x, φx, ψx)| = f , and conse- quently we have Ahmad and Nieto Boundary Value Problems 2011, 2011:36 http://www.boundaryvalueproblems.com/content/2011/1/36 Page of...
... differential equationsand systems The history and development of this question is explained in the work of Horgan and Knowles [1] The interested reader is referred to the papers [2-9] and the reviews ... parabolic equations with nonlinear boundary conditions, (see also [16,17]) Under nonlinear dissipative feedbacks on the boundary, Nouria [18] proved a polynomial stability for regular initial data and ... bounded and unbounded feedbacks for some evolution equations Recently, Celebi and Kalantarov [21] established a Phragmén-Lindelöf type theorems for a linear wave equation under nonlinear boundary conditions...
... S Li, Y Wang, and X Xue, “Multiple solutions for semilinear elliptic equations with Neumann boundary condition and jumping nonlinearities,” Journal of Mathematical Analysis and Applications, ... Differential Equationsand 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, ... Li, Y Ding, and S Li, “Multiple solutions of nonlinear elliptic equations for oscillation problems,” Journal of Mathematical Analysis and Applications, vol 303, no 2, pp 477–485, 2005 Boundary...
... Khemmoudj, and M Medjden, “Uniform stabilization of the damped CauchyVentcel problem with variable coefficients and dynamic boundary conditions, ” Journal of Mathematical Analysis and Applications, ... Lions and E Magenes, Nonhomegeneous Boundary Value Problems and Applications, Springer, New York, NY, USA, 1972 33 Y Li, “Basic inequalityies and the uniqueness of the solutions for differential equations, ” ... the theorem of existence and uniqueness,” Archive for Rational Mechanics and Analysis, vol 24, pp 352–362, 1967 T Hintermann, “Evolution equations with dynamic boundary conditions, ” Proceedings...
... the limits u tj , u t− , and j Boundary Value Problems j 1, 2, , p exist, and impulsive conditionsandboundaryconditions in problem 1.1 hold, we say it is a classical solution of problem ... Qian and X Li, “Periodic solutions for ordinary differential equations with sublinear impulsive effects,” Journal of Mathematical Analysis and Applications, vol 303, no 1, pp 288–303, 2005 L Chen and ... “Nonlinear boundary value problem of first order impulsive functional differential equations, ” Journal of Mathematical Analysis and Applications, vol 318, no 2, pp 726–741, 2006 10 J J Nieto and D O’Regan,...
... 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, ” ... Mathematical Analysis and Applications, vol 321, no 2, pp 751–765, 2006 12 M Feng, D Ji, and W Ge, “Positive solutions for a class of boundary- value problem with integral boundaryconditions in Banach ... but difficult Professors Wei 16, 17 , Du and Zhao 18 , Graef and Kong 19 , Zhang and Liu 20 , and others have done much excellent work under some suitable conditions in this direction To the author’s...
... direct method for solving difference equationsand an iterative method for solving the grid equations of a general form and their application to difference equations are considered in 11, 12 Various ... three-pointwise equations are described Also, modern economic direct methods for solving Poisson difference equations in a rectangle with boundaryconditions of various types are stated Chung and Yau ... 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 boundary conditions...
... and O I Marichev, Fractional Integrals and Derivatives, Gordon and Breach Science, Yverdon, Switzerland, 1993 I Podlubny, Fractional Differential Equations, vol 198 of Mathematics in Science and ... 10 Advances in Difference Equations A A Kilbas, H M Srivastava, and J J Trujillo, Theory andApplications of Fractional Differential Equations, vol 204 of North-Holland Mathematics Studies, Elsevier ... Dordrecht, The Netherlands, 2007 V Daftardar-Gejji and S Bhalekar, Boundary value problems for multi-term fractional differential equations, ” Journal of Mathematical Analysis and Applications, vol...
... ≥ , and m % ∑ u ( t, x ) − u ( t, x ) i i r dx , i =1 (u (t, x ) , v (t, x )) and j =1 are the solutions of drive-response systems (1) and (4) satisfying boundaryconditionsand initial conditions ... time-varying and distributed delays and reaction-diffusion terms by using Poincaré integral inequality, Young inequality technique, and Lyapunov method, which are very important in theories andapplications ... smooth boundary ∂Ω and T ; u = ( u1 , u2 , , um ) ∈ m T , v = ( v1 , v2 , , ) ∈ n , ui ( t , x ) and v j ( t , x ) represent the states of the ith neurons and the jth neurons at time t and in...
... the periodic and antiperiodic boundaryconditions They found out the following results Advances in Difference Equations see 4, Theorems 2.2 and 3.1 : the periodic and antiperiodic boundary value ... Dordrecht, The Netherlands, 1997 18 Advances in Difference Equations Y Wang and Y Shi, “Eigenvalues of second-order difference equations with periodic and antiperiodic boundary conditions, ” Journal ... 1, he viewed the boundaryand they may not be all distinct If c−1 conditions 1.4 as the periodic boundaryconditions for 1.5 Shi and Chen investigated the more general boundary value problem −∇...
... Cheung and J Ren, “Discrete non-linear inequalities andapplications to boundary value problems,” Journal of Mathematical Analysis and Applications, vol 319, no 2, pp 708–724, 2006 13 W N Li and ... Analysis and Applications, vol 189, no 1, pp 128–144, 1995 15 P Y H Pang and R P Agarwal, “On an integral inequality and its discrete analogue,” Journal of Mathematical Analysis and Applications, ... Mathematical Analysis and Applications, vol 252, no 2, pp 864–878, 2000 B G Pachpatte, Inequalities for Differential and Integral Equations, vol 197 of Mathematics in Science and Engineering, Academic...
... we can find ω and φ such that c + ω ≥ 0, Ω k(x; y)φ(y) d y < 1, (2.19) where c and φ are defined in (2.6) and (2.9), and the functions β, α, and k also satisfy some corresponding conditions as ... parabolic equations with nonlocal boundary conditions, ” Journal of Mathematical Analysis and Applications, vol 294, no 2, pp 712–728, 2004 [2] C V Pao, “Dynamics of reaction-diffusion equations ... of Mathematical Analysis and Applications, vol 185, no 1, pp 161–174, 1994 [7] Y Wang and B Nai, “Existence of solutions to nonlocal boundary problems for parabolic equations, ” Chinese Annals...