On the continuous dependence of solutions of boundary value problems for ordinary differential equations

Uniqueness of solutions for fourth-order nonlocal boundary value problems

“…It is then established that solutions of both (1.1), (1.2) and (1.1), (1.3) are also unique. Fundamental to our arguments is a Kamke type of convergence result for boundary value problems due to Vidossich [42], as well as a precompactness condition on bounded sequences of solutions of (1.1) due to Jackson and Schrader; see Agarwal [1]. We state both of those results at the outset of the section.…”

Existence of solutions for three-point boundary value problems for second order equations

“…Our arguments involve an application of a Kamke-like result due to Vidossich [19] as it applies to solutions of (1), (3). (1), conditions (A), (B), and (C) are satisfied.…”

“…In Section 3, we make use of the continuous dependence result, the existence of solutions of (1), (3), and a Kamke-like result due to Vidossich [19] for solutions of (1), (3), to yield existence of solutions of (1), (2). The paper is completed with a corollary illustrating that, if f (x, v 1 , v 2 ) satisfies certain monotonicity conditions with respect to v 1 , then the crucial condition (C) is satisfied.…”

A note on the dependence of solutions on functional parameters for nonlinear Sturm-Liouville problems

“…In the wide literature devoted to BVPs similar to (1.1)-(1.3) (see e.g. [4][5][6][7][8][9][10][11][12][13][17][18][19][20][21] and references therein) the authors investigate mainly the existence of solutions for (1.1) under a variety of boundary conditions. Moreover, in the last fifty years, we could observe increasing interest in investigating sufficient conditions for the oscillation or nonoscillation of solutions of various classes of ODEs ( [1][2][3][5][6][7][8][9], and references therein).…”

“…Moreover, in the last fifty years, we could observe increasing interest in investigating sufficient conditions for the oscillation or nonoscillation of solutions of various classes of ODEs ( [1][2][3][5][6][7][8][9], and references therein). We have to also recall results due 838 Aleksandra Orpel to G. Vidossich who considered the continuous dependence of solutions for general boundary value problems (see [20,Theorem 1]). The author assumed, among others, that the limit problem possesses at most one solution.…”