boundary value problems for partial differential equations

... This page intentionally left blank Perturbation of the Boundary in Boundary- Value Problems of Partial Differential Equations LONDON MATHEMATICAL SOCIETY LECTURE NOTE SERIES Managing ... Mathematical Society Lecture Note Series 318 Perturbation of the Boundary in Boundary- Value Problems of Partial Differential Equations Dan Henry with editorial assistance from Jack Hale and Antˆonio ... Euler-Jacobi inversion formula and asymptotics beyond all orders, V KOWALENKO et al Number theory 1992–93, S DAVID (ed) Stochastic partial differential equations, A ETHERIDGE (ed) Quadratic forms with applications

Ngày tải lên: 04/03/2019, 11:09

... boundary value problems for nonlinear impulsive fractional differential equations is still in the initial stages Ahmad and Sivasundaram 15, 16 studied the following impulsive hybrid boundary value ... Advances in Difference Equations Volume 2011, Article ID 404917, 16 pages doi:10.1155/2011/404917 Research Article Nonlocal Boundary Value Problem for Impulsive Differential Equations of Fractional ... noteworthy papers dealing with the nonlocal boundary value problem of fractional differential equations Benchohra et al 12 investigated the following nonlocal boundary value problem c Dα u t f t, u t u0

Ngày tải lên: 21/06/2014, 07:20

... established the solvability of initial value problems (IVPs) and periodic boundary- value problems (BVPs) for this special class of SDEs The index notion for linear SDEs with time-varying coefficients ... optimal control problems and so forth (see [6, 7]) On the other hand, SDEs occur in a natural way of using discretization techniques for solving DAEs and partial differential- algebraic equations ... decomposing it into an ordinary differential equation and algebraic relations Results on the solvability of the Cauchy problem for (2) can be found in [10]; for the boundary value problems, we can refer

Ngày tải lên: 16/12/2017, 10:52

... Iterative method for solving boundary value problems for the nonlinear fourth-order differential equations Boundary value problems for the nonlinear fourth order equations with dif-ferent boundary ... Luong Tai, etc also studied methods for solving the boundary value problems for differential equations Among the differential equations, the nonlinear fourth-order differential equation has been ... theorems; the monotone method for solving boundary value problem of differ-ential equations; Green function for some problems and numerical methods for solving differential equations The basic knowledge

Ngày tải lên: 01/04/2021, 19:17

... Ge, Boundary Value Problems of Nonlinear Differential Equations, Science Publications, Beijing, 2007 [13] J.R Graef, J Henderson, Double solutions of boundary value problems for 2mth-order differential ... solutions for a boundary value problem for difference equations, J Difference Equ Appl (1995), 262–270 [23] H Pang, H Feng, W Ge, Multiple positive solutions of quasi-linear boundary value problems for ... substantial results have been obtained for positive solutions and multiple positive solutions for boundary value problems for finite difference equations; see, for example [2, 5, 10, 11, 13, 15,

Ngày tải lên: 23/10/2022, 17:38

... Corporation Boundary Value Problems Volume 2009, Article ID 541435, 11 pages doi:10.1155/2009/541435 Research Article Antiperiodic Boundary Value Problems for Finite Dimensional Differential ... May 2009 Recommended by Juan J Nieto We study antiperiodic boundary value problems for semilinear differential and impulsive differential equations in finite dimensional spaces Several new existence ... we consider the antiperiodic boundary value problem u t Gu t u Δu tk a.e t ∈ J f t, u t , 0, T , t / tk , −u T , I k u tk , k E 1.2 1, 2, , p, Boundary Value Problems where G : Rn → Rn is

Ngày tải lên: 01/11/2022, 08:31

... Ma and Yan Boundary Value Problems (2017) 2017:9 DOI 10.1186/s13661-016-0744-y RESEARCH Open Access Positive global solutions of nonlocal boundary value problems for the nonlinear convection ... the monotone iterative scheme for elliptic boundary value problems is based on a positivity lemma which plays a fundamental role in nonlinear elliptic boundary value problems A lemma (cf []) under ... positive solutions Ma and Yan Boundary Value Problems (2017) 2017:9 Page of 13 Positive global solutions of nonlocal functional reaction-diffusion boundary value problems In this section we go

Ngày tải lên: 04/12/2022, 16:04

... types of problems are well-posed These include boundary value problems for (stationary) elliptic partial di erential equations and initial -boundary value problems for (time-dependent) equations ... its applications to solve initial -boundary value problems for partial di erential equations Chapters V and VI provide the immediate extensions to cover evolution equations of second order and of ... treatment of certain elliptic boundary value problems by the classical Dirichlet principle Then we brie y discuss certain unilateral boundary value problems, optimal control problems, and numerical

Ngày tải lên: 31/03/2014, 15:56

... ∥k∥2L2 (0,∞;L2 (Ω)) ∗ 48 The first initial -boundary value problem for semilinear hyperbolic equations REFERENCES [1] Evans L.C., 1997 Partial differential equations AMS [2] Robert A.Adam, 1975 Sobolev ... (2.22) 44 The first initial -boundary value problem for semilinear hyperbolic equations ( ) On the other hand, from (1.8) then f (x, t, uN , DuN ) − f (x, t, ω, Dω), uN − ω ≥ for ∀ω ∈ H01 (Ω) Integrating ... initial -boundary value problem for semilinear hyperbolic equations N N 2 Now setting η(t) = ∥uN t ∥L2 (Ω) + A[u , u ; t], ψ(t) = ∥h∥L2 (Ω) + ∥k∥L2 (Ω) , then (2.14) will be written in the form

Ngày tải lên: 25/11/2020, 23:24

... closed form The theorem is proved References Gakhov, F.D.: Boundary value problems, Oxford, 1966 (3rd Russian complemented and corrected edition, Moscow, 1977) Mau, Ng.V.: Boundary value problems ... is a boundary value of the function GðzÞ in DÀ In the sequel, for every function ctị A X , we write Kc jịtị ẳ cðtÞjðtÞ: ð4Þ On Solvability of a Boundary Value Problem for Singular Integral Equations ... solvability of boundary value problems for singular integral equations of the form (i)–(ii) By an algebraic method we reduce the problem (i)–(ii) to a system of linear algebraic equations which

Ngày tải lên: 19/10/2022, 18:31

... Fredholm boundary value problem for system 3.1 3.8 Advances in Difference Equations 3.1 Fredholm Boundary Value Problem Using the results in 8, , it is easy to derive statements for a general boundary ... next step from the solvability condition of the boundary value problem for z1 t Advances in Difference Equations 15 For ε1 , we get the boundary value problem k z1 t ˙ A Sh0 z1 t B t Sh z0 t Bi ... Fredholm Boundary- Value Problems, VSP, Utrecht, The Netherlands, 2004 10 A A Boichuk, J Dibl´k, D Ya Khusainov, and M Ruˇ iˇ kov´ , “Fredholm’s boundary- value problems ı a ˚z c for differential...

Ngày tải lên: 21/06/2014, 16:20

... of boundary value problems, such as the ones associated to advanced, or delayed difference equations, or sum difference equations Several approaches can be used in order to treat boundary value problems ... space has to be chosen for solving boundary value problems related to existence of unbounded solutions Remark 2.4 If B is closed, as it often happens for boundary value problems on finite discrete ... BVPs for functional difference equations [9] J R Graef and J Henderson, Double solutions of boundary value problems for 2mth-order differential equations and difference equations, Computers & Mathematics...

Ngày tải lên: 22/06/2014, 22:20

... even in the case when h t ≤ g t for t ∈ 0, ∞ Maximum Boundaries Principles in Existence and Uniqueness of Boundary Value Problems Consider the boundary value problems of the following type Mx ... 1.8 be positive for ≤ s ≤ t ≤ ω, then the Cauchy function C t, s of 1.1 is also positive for ≤ s ≤ t ≤ ω This result was extent on various boundary value problems in 16 in the form: Let the operator ... of solutions of various boundary value problems for first order functional differential equations were obtained All results presented in the paper 15 and in the book 16 for equation with the difference...

Ngày tải lên: 22/06/2014, 03:20

... multi-point boundary value problem, Annali di Matematica Pura ed Ap[4] plicata Series IV 86 (1970), 367–399 [5] I Kiguradze, Some singular boundary value problems for ordinary differential equations, ... singular boundary value problems for functional differential equations of higher order, Georgian Mathematical Journal (2001), no 4, 791–814 [11] I T Kiguradze and B L Shekhter, Singular boundary value ... optimal conditions for the solvability of two-point singular boundary value problems, [6] Functional Differential Equations 10 (2003), no 1-2, 259–281, Functional differential equations and applications...

Ngày tải lên: 23/06/2014, 00:20

... time, the boundary value problems for impulsive differential equations and impulsive difference equations have received much attention [4–18] On the other hand, recently, the theory of dynamic equations ... result for impulsive dynamic equations on time scales Appl Math Lett 20, 206–212 (2007) [27] Geng, F, Xu, Y, Zhu, D: Periodic boundary value problems for first-order impulsive dynamic equations ... dynamic equations on time scales J Math Anal Appl 324, 425–434 (2006) 18 [25] Chen, HB, Wang, HH: Triple positive solutions of boundary value problems for pLaplacian impulsive dynamic equations...

Ngày tải lên: 21/06/2014, 17:20

... boundary value problems of impulsive differential equations, ” Applicable Analysis, vol 44, no 3-4, pp 145–158, 1992 19 D.-B Wang, “Positive solutions for nonlinear first-order periodic boundary value problems ... impulsive dynamic equations on time scales,” Journal of Difference Equations and Applications, vol 10, no 6, pp 541–548, 2004 F Geng, Y Xu, and D Zhu, “Periodic boundary value problems for first-order ... differential equations, ” Journal of Mathematical Analysis and Applications, vol 325, no 1, pp 226–236, 2007 13 X Liu, “Nonlinear boundary value problems for first order impulsive integro-differential equations, ”...

Ngày tải lên: 21/06/2014, 20:20

... Therefore we have u t p − λ Σi Ii ui ti T t Gu s f s ds λ G us f s ds 3.11 for t ∈ 0, t1 , and u t p − λ Σi Ii ui ti T Gu s t λ G us f s ds f s ds λ Σk Ii ui ti i 3.12 Boundary Value Problems for ... has a solution For the uniqueness, if u · , v · are two solutions of E 2.2 , set w t Aw t , and w t −w t T , for t ∈ R Following the obvious u t − v t , then w t Boundary Value Problems gives ... conditions on G, f, and function, Δu tk k Ik u for k 1, 2, , p, we prove an existence result for E 1.2 Antiperiodic Problem for Differential Equations in Rn Let | · | be the norm in Rn In...

Ngày tải lên: 21/06/2014, 20:20

... 19, no 10, pp 1019–1023, 2006 Y Liu and W Ge, “Twin positive solutions of boundary value problems for finite difference equations with p-Laplacian operator,” Journal of Mathematical Analysis and ... difference equations, ” Science in China Series A, vol 33, no 3, pp 226–235, 2003 L Jiang and Z Zhou, “Existence of nontrivial solutions for discrete nonlinear two point boundary value problems, ” ... Δx k − z k k for any x, z ∈ H Noticing the fact that x J x z for any x, z ∈ H lim t→0 J x x T tz − J x t for any x ∈ H again, we obtain T f k, x k z k k 2.7 Advances in Difference Equations Remark...

Ngày tải lên: 22/06/2014, 19:20

... ᏿ᐃα -functional is the coercivity lemma proved in [3] 78 Boundary value problems for the ᏿ᐃα -equations (A,φ) Lemma 2.5 (coercivity) For each (A,φ) ∈ Ꮿα , there exist g ∈ Ᏻα and a constant KC ... = (3.42) 86 Boundary value problems for the ᏿ᐃα -equations Regularity of the solution (A,φ) Let β = {ei ; ≤ i ≤ 4} be an orthonormal frame fixed on TX with the following properties; for all i, ... argument Appendix Estimates for solutions of 3rd-degree equation Let p, q ∈ R and consider the equation x3 + px + q = (A.1) 90 Boundary value problems for the ᏿ᐃα -equations Proposition A.1 The...

Ngày tải lên: 23/06/2014, 00:20

... development of boundary value problems for differential equations [1–5], dif- ference equations [6, 7], and the theory of time scales [8–12], the existence of solutions for boundary value problems on ... results for some second-order four-point boundary- value problems Nonlinear Anal 60, 491–500 (2004) [4] Yang, L, Liu, X, Jia, M: Multiplicity results for second-order m-point boundary value problem ... Positive solutions for a nonlinear three-point boundary value problem Electron J Diff Equ 34, 1–8 (1999) [2] Ma, R, Cataneda, N: Existence of solution for nonlinear m-point boundary value problem J...

Ngày tải lên: 21/06/2014, 17:20