A Uniqueness Theorem for a Boundary Value Problem

Abstract

Abstract.In this paper it is proved that the two-point boundary value problem, namely (d(4)/dx4 + f)y = g, y(0) -Ax = y(l) -A2 = y"(0) -Bx = y "(I) -B2 = 0, has a unique solution provided infxf(x) = --n > -it4. The given boundary value problem is discretized by a finite difference scheme. This numerical approximation is proved to be a second order convergent process by establishing an error bound using the L2-norm of a vector.

Fourth order singular p-Laplacian differential equations with integral boundary conditions

“…f is continuous, problem (1.7) is nonsingular, the existence and uniqueness of positive solutions of (1.7) have been studied by papers [15][16][17][18].…”

Nonresonant singular fourth-order boundary value problems

“…Owing to its importance in physics, the existence of solutions to this nonsingular problem has been studied by many authors; see for example [1][2][3][4][5][6][7][8][9][10][11]. However, in practice only its positive solutions are significant.…”

Higher-order Lidstone boundary value problems for elliptic partial differential equations

“…[1][2][3][4][5][6][7][8][9][10][11][12][13][15][16][17][18][19][20][21]23,24,26,27]). Most of the discussions are devoted to the two-point Lidstone boundary value problem:…”

“…, D 2(n−1) u), 0 < x < 1, D 2i u(0) = D 2i u(1) = 0, 0 i n − 1, (1.1) where Du ≡ du/dx, n 1 and f is a continuous function of its arguments (cf. [1][2][3][5][6][7][8][9][10][11][12][13][17][18][19][20]24,26]). The discussions in these works are mainly concerned with the existence and multiplicity of solutions using different methods.…”

“…On the other hand, there are also a few papers that are devoted to the uniqueness problem but only for lower-order problems (cf. [1,2,9,17,26]) or for the case where f depends only on u and not on any derivative of u (cf. [3]).…”