On the boundary conditions associated with second-order linear homogeneous differential equations

J. Das

Displaying similar documents to “On the boundary conditions associated with second-order linear homogeneous differential equations”

Boundary value problems with compatible boundary conditions

George L. Karakostas, P. K. Palamides (2005)

Czechoslovak Mathematical Journal

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If $Y$ is a subset of the space $ℝ^{n} \times ℝ^{n}$ , we call a pair of continuous functions $U$ , $V$ $Y$ -compatible, if they map the space $ℝ^{n}$ into itself and satisfy $U x \cdot V y \geq 0$ , for all $(x, y) \in Y$ with $x \cdot y \geq 0$ . (Dot denotes inner product.) In this paper a nonlinear two point boundary value problem for a second order ordinary differential $n$ -dimensional system is investigated, provided the boundary conditions are given via a pair of compatible mappings. By using a truncation of the initial equation and restrictions of its...

On the uniqueness of positive solutions for two-point boundary value problems of Emden-Fowler differential equations

Satoshi Tanaka (2010)

Mathematica Bohemica

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The two-point boundary value problem $u^{''} + h (x) u^{p} = 0, a < x < b, u (a) = u (b) = 0$ is considered, where $p > 1$ , $h \in C^{1} [0, 1]$ and $h (x) > 0$ for $a \leq x \leq b$ . The existence of positive solutions is well-known. Several sufficient conditions have been obtained for the uniqueness of positive solutions. On the other hand, a non-uniqueness example was given by Moore and Nehari in 1959. In this paper, new uniqueness results are presented.

Some dimensional results for a class of special homogeneous Moran sets

Xiaomei Hu (2016)

Czechoslovak Mathematical Journal

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We construct a class of special homogeneous Moran sets, called ${m_{k}}$ -quasi homogeneous Cantor sets, and discuss their Hausdorff dimensions. By adjusting the value of ${m_{k}}_{k \geq 1}$ , we constructively prove the intermediate value theorem for the homogeneous Moran set. Moreover, we obtain a sufficient condition for the Hausdorff dimension of homogeneous Moran sets to assume the minimum value, which expands earlier works.