On a class of functional boundary value problems for third-order functional differential equations with parameter

Staněk, Svatoslav

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 31 (1992) no. 1, pp. 71-82

Détail

Classification : 34B15, 34K10

Bibliographie

[1] A.R. Aftabizadeh, J. Wiener: Existence and uniqueness theorems for third order boundary value problems. Rend. Sem. Mat. Univ. Padova, 75, 1986, 130-141. | MR | Zbl

[2] R.P. Agarwal, R.P. Krissnamurthy: On the uniqueness of solution of nonlinear boundary value problems. J. Math. Phys. Sci. 10, 1976, 17-31. | MR

[3] R.P. Agarwal: On boundary value problems for y''' =f(x,y,y',y'´). Bull. of the Institut of Math. Acad. Sinica, 12, 1984, 153-157. | MR

[4] J. Andres: On a boundary value problem for x'''=f(t,x,x',x''). Acta UPO, Fac. rer. nat., Vol.91, Math. XXVII, 1988, 289-298. | MR | Zbl

[5] D. Barr, T. Sherman: Existence and uniqueness of solutions of three point boundary value problems. J. Diff. Eqs., 13, 1973, 197-212. | MR | Zbl

[6] J. Bebernes: A sub-function approach to boundary value problems for nonlinear ordinary differential equations. Pacific J. Math. 13, 1963, 1063-1066. | MR

[7] S.A. Bespalova, J.A. Klokov: A three-point boundary value problem for a third order nonlinear ordinary differential equations. (in Russian). Differenciaľnye Uravnenija, 12, 1976, 963-970. | MR

[8] G. Carristi: A three-point boundary value problem for third order differential equation. Boll.Unione Mat. Ital., C4, 1, 1985, 259-269.

[9] K.M. Das, B.S. Lalli: Boundary value problems for y' ' ' = f(x,y,y' ,y' ' ). J. Math. Annal. Appl., 81, 1981, 300-307. | MR | Zbl

[10] A. Granas R. Guenther, L. Lee: Nonlinear Boundary Value Problems for Ordinary Differential Equations. Polish Acad. of Sciences, 1985.

[11] M. Greguš: Third Order Linear Differential Equtation. Veda 1981 (Slovak), Bratislava. | MR

[12] C.P. Gupta: On a third-order three-point boundary value problem at rezonance. Diff. Int. Equations, Vol.2, 1 (1989),1-12. | MR

[13] J. Henderson, L. Jackson: Existence and uniqueness of solutions of k-point boundary value problems for ordinary differential equations. J. Diff. Eqs., 48, 1970, 373-385. | MR

[14] J. Henderson: Best interval lengths for boundary value problems for third order Lipschitz equations. SIAM J. Math. Anal.,18, 1987, 293-305. | MR | Zbl

[15] L. Jackson, K. Schrader: Subfunctions and third order differential inequalities. J. Diff. Eqs., 8, 1970, 180-194. | MR | Zbl

[16] L. Jackson, K. Schrader: Existence and uniqueness of solution of boundary value problems for third order differential equations. J. Diff. Eqs., 9, 1971, 46-54. | MR

[17] L. Jackson: Existence and uniqueness of solutions of boundary value problems for third order differential equations. J. Diff. Eqs., 13, 1973, 432-437. | MR | Zbl

[18] I.T. Kiguradze: Boundary Problems for Systems of Ordinary Differential Equations. (in Russian). Itogi nauki i tech..Sovr. problemy mat., 30, Moscow 1987. | MR

[19] G.A. Klassen: Differential inequalities and existence theorems for second and third order boundary value problems. J. Diff. Eqs., 10, 1971, 529-537. | MR

[20] G.A. Klassen: Existence theorems for boundary value problems for n-th order ordinary differential equation. Rocky Mountain J. Math., 3, 1973, 457-472. | MR

[21] E. Lepina, A. Lepin: Existence of a solution of the three-point BVP for a non-linear third order ordinary differential equation. (in Russian). Latv. Mat. Ezheg., 4, 1968, 247-256.

[22] E. Lepina, A. Lepin: Necessary and sufficient conditions for existence of a solution of a three-point BVP for a nonlinear third order differential equation. (in Russian). Latv. Mat. Ezheg., 8, 1970, 149-154.

[23] K.N. Murthy, K.S. Rao: On existence and uniqueness of solutions of two and three point boundary value problems. Bull.Calcutta Math. Soc., 73, 3 (1981), 165-172. | MR

[24] K.N. Murthy, C.N. Prasad: Three-point boundary value problems, existence and uniqueness. Yokohama Math. J., 29, 1981, 101-105. | MR

[25] B.G. Pachpatte: On a certain boundary value problem for third order differential equations. An. Sti.Univ. "Al.I.Cuza" Iasi Sect. Ia Mat, XXXXII, 1, 1986, 55-61. | MR | Zbl

[26] L.I. Pospelov: Necessary and sufficient conditions for existence of a solutions for some BVPs for the third order nonlinear ordinary differential equation. (in Russian). Latv. Math. Ezheg., 8, 1970, 205-213.

[27] D.J. O’Regan: Topological transversality. Applications to third order boundary value problems. SIAM J. Math. Anal., 18, 1987, 630-641. | MR

[28] J. Rusnák: A three-point boundary value problem for third order differential equations. Math. Slovaca, 33, 1983, 247-256. | MR

[29] J. Rusnák: Method of successive approximations for certain non-linearthird order boundary value problem. Acta UPO, Fac. rer. nat., Math. XXVI, 88, 1987, 161-168. | MR

[30] J. Rusnák: Constructions of lower and upper solutions for a nonlinear boundary value problem of the third order and their applications. Math. Slovaca, 40, No.1, 1990, 101-110. | MR

[31] S. Staněk: Three-point boundary value problem for nonlinear third-order differential equations with parameter. Acta UPO, Fac. rer. nat., Math. XXX, (1991) 61-74. | MR

[32] S. Staněk: Three point boundary value problem for nonlinear second-order differential equations with parameter. Czech.Math. J. 42 (117), 1992, 241-256. | MR

[33] S. Staněk: On a class of five-point boundary value problems in second-order functional differential equations with parameter. (to appear). | MR

[34] N.I. Vasilev, J.A. Klokov: Elements of the Theory of Boundary Value Problems for Ordinary Differential Equations. (in Russian). Riga 1978.