References [1] GUSTAFSON, G. B.-RIDENHOUR, J. R.: Lower order branching and conjugate function discontinuity , J. Differential Equations 27 (1978), 167-179. [2] GUSTAFSON, G. B.-RIDENHOUR, J. R.: Uniqueness intervals for multipoint boundary value problems (preprint 2008). [3] HARTMAN, P.: Unrestricted n-parameter families , Rend. Circ. Mat. Palermo (2) 7 (1958), 123-142. [4] HARTMAN, P.: Ordinary Differential Equations, John Wiley and Sons, Inc., New York, 1964. [5] MIKUSI ´NSKI, J.: Sur l’´equation x ( n ) + A ( t ) x = 0, Ann. Polon. Math. 1 (1955

References [1] A. Ashyralyev, O. Gercek: Nonlocal boundary value problem for elliptic-parabolic differential and difference equations. Discrete Dyn. Nat. Soc. (2008) 16p. [2] R. Beals: Nonlocal Elliptic Boundary Value Problems. Bull. Amer. Math. Soc. 70 (5) (1964) 693-696. [3] V. Beridze, D. Devadze, H. Meladze: On one nonlocal boundary value problem for quasilinear differential equations. In: Proceedings of A. Razmadze Mathematical Institute. (2014) 31-39. [4] G. Berikelashvili: Construction and analysisi of difference schemes of the rate convergence. Memoirs

. – Oxford University Press. [11] Gasparo M.G. and Macconi M. (1990): Initial value methods for second-order singularly perturbed boundary-value problems. – Journal of Optimization Theory and Applications, vol.66, pp.197-210. [12] Gasparo M.G. and Macconi M. (1989): New initial-value method for singularly perturbed boundary-value problems . – Journal of Optimization Theory and Applications, vol.63, pp.213-224. [13] Gasparo M.G. and Macconi M. (1992): Numerical solution of second-order nonlinear singularly perturbed boundary-value problems by initial value methods

References [1] AZBELEV, N. V.-MAKSIMOV, V. P.-RAKHMATULLINA, L. F.: Introduction to the Theory of Functional Differential Equations . Nauka, Moscow, 1991. (In Russian) [2] HAKL, R.-LOMTATIDZE, A.-ˇSREMR, J.: On an antiperiodic type boundary-value problem for first order nonlinear functional differential equations of non-Volterra’s type, Nelinijni Kolyvannya 6 (2003), No. 4, 550-573. [3] HAKL, R.-LOMTATIDZE, A.-ˇSREMR, J.: Some Boundary Value Problems for First Order Scalar Functional-Differential Equations. Folia Fac. Sci. Natur. Univ. Masaryk. Brun. Math

-value problems for differential systems with a single delay, Nonlinear Anal. 72 (2010). 2251 2258. [5] VISHIK. V. I. LYUSTERNIK. L. A.: Solution of some perturbation problems in the case of matrices and self-adjoint and. non self-adjoint differential equations, Uspekhi Mat. Nank. 15 (I960). 3-80. (In Russian) [6] BOICHUK. A.-DIBLIK. J. KHUSAINOV. D. RUŽIČKOVĀ. M.: Boundary-value problems for delay differential systems, Adv. Difference Equ. 2010 (2010). 20 p.

References Berinde, V. - Existence and approximation of solutions of some first order iterative differential equations , Miskolc Math. Notes, 11 (2010), 13-26. Berinde V. - Iterative Approximation of Fixed Points , Second edition, Lecture Notes in Mathematics, 1912, Springer, Berlin, 2007. Benchohra, M.; Hamani, S. - Boundary value problems for differential equations with fractional order and nonlinear integral conditions , Comment. Math., 49 (2009), 147-159. Buică, A. - Existence continuous dependence of solutions of some functional-differential equations

References [1] Sung N.Ha., A nonlinear shooting method for two-point boundary value problems , Comp. and Math. with Appl., 42, 2001, 1411–1420. [2] Filipowska R., An iterative shooting method for the solution of higher order boundary value problems with additional boundary conditions , Solid State Phenomena, 235, 2015, 31–36. [3] Filipowska R., Variational iteration technique for solving higher order boundary value problem with additional boundary conditions , Technical Transactions, 4- M/2016, 15–20. [4] Noor A.M., Mohyud–Din S.T., Variational iteration

], Homotopy Analysis Method (HAM) [ 2 , 4 ], Variational Iteration Method (VIM) [ 7 , 18 ], Galerkin’s Method [ 1 , 8 , 9 , 11 , 13 , 17 , 19 , 20 , 21 ]. Besides, there is various solution techniques for Schrödinger equation. In this paper, we regard a first type boundary value problem for linear Schrödinger equation in the form: (1.1) i ∂ ψ ∂ t + a 0 ∂ 2 ψ ∂ x 2 + i a 1 ( x , t ) ∂ ψ ∂ x − a 2 ( x ) ψ + v ( t ) ψ = f ( x , t ) i\frac{{\partial \psi }}{{\partial t}} + {a_0}\frac{{{\partial ^2}\psi }}{{\partial {x^2}}} + i{a_1}(x,t)\frac{{\partial \psi

.—INGALLS, S.—KIM S. H.—LADNER, R.— MARKS, K.—NELSON, S.—PHARAOH, A.—TRIMMER, R.—ROSENBERG, J. VON, WALLACE, G.—WEATHERALL, P.: Global bathymetry and elevation data at 30 arc seconds resolution: SRTM30 PLUS , Marine Geodesy 32 (2009), no. 4, 355–371. [4] BITZADSE, A. V.: Boundary-Value Problems for Second-Order Elliptic Equations .North-Holland, Amsterdam, 1968. [5] BJERHAMMAR, A.—SVENSSON, L.: On the geodetic boundary value problem for a fixed boundary surface, A satellite approach , Bull Geod. 57 (1983), no. 1–4, 382–393. [6] BRENNER, S. C.—SCOTT, L. R.: The

References [1] Ravi P. Agarwal, Positive solutions for Dirichlet problems of singular nonlinear fractional differential equations., Journal of Mathem. Anal. and Applications, 371, (2010), 57-58. [2] Ravi P. Agarwal, Boundary value problems for differential equations involving Riemann-Liouville fractional derivative on the half line., Dynamics of Continuous Discrete and Impulsive System, 18, (2011), 235-244. [3] Zhanbig Bainov, Positive solutions for boundary value problem of nonlinear frac- tional differential equation, Journal of Mathematical Anal and