Loading...
Please wait, while we are loading the content...
Similar Documents
Existence and uniqueness of solutions of multipoint boundary value problems for ordinary differential equations
| Content Provider | Semantic Scholar |
|---|---|
| Author | Gewert, Marian |
| Copyright Year | 1993 |
| Abstract | (0.1) x′ = f(t, x) , x = (x1, . . . , xn), (0.2) xs(t1) = αm , xj(τ) = αj , xr(t2) = αp (j = 1, . . . , n, j 6= m, p, m 6= p) where f : [t1, t2] × R → R, τ ∈ [t1, t2], s,m, r, p ∈ {1, . . . , n}, n ≥ 3, and α = (α1, . . . , αn) ∈ R. Specifically, we present conditions where some restriction on the signs of the entries in the Jacobian matrix of f plays a role. In [8] the author has given such a criterion for a certain class of two-point boundary value problems for Eq. (0.1). The first results of this nature were established by Garner [5, 6] and Garner and Burton [7]. Their theorems only concern the situation when (0.1) is linear and (s,m, r, p) = (1, 1, n, n). Results in the same spirit, with an nth-order (n ≥ 3) differential equation in place of (0.1), have been obtained in [4] for linear cases and in [1, 2, 9] for nonlinear cases. The principal result of the present paper is Theorem 3.1, which generalizes the theorems in [5–7]. One can also derive as applications of this theorem various results which, in some cases, improve the theorems in [1, 2, 4, 9]. These applications are presented in the last section. |
| Starting Page | 253 |
| Ending Page | 264 |
| Page Count | 12 |
| File Format | PDF HTM / HTML |
| DOI | 10.4064/cm-64-2-253-264 |
| Volume Number | 64 |
| Alternate Webpage(s) | http://matwbn.icm.edu.pl/ksiazki/cm/cm64/cm64212.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
