Existence results for a class of high order differential equation associated with integral boundary conditions at resonance

Le Cong Nhan; Do Huy Hoang; Le Xuan Truong

Displaying similar documents to “Existence results for a class of high order differential equation associated with integral boundary conditions at resonance”

Dimension in algebraic frames, II: Applications to frames of ideals in $C (X)$

Jorge Martinez, Eric R. Zenk (2005)

Commentationes Mathematicae Universitatis Carolinae

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This paper continues the investigation into Krull-style dimensions in algebraic frames. Let $L$ be an algebraic frame. $dim (L)$ is the supremum of the lengths $k$ of sequences $p_{0} < p_{1} < \dots < p_{k}$ of (proper) prime elements of $L$ . Recently, Th. Coquand, H. Lombardi and M.-F. Roy have formulated a characterization which describes the dimension of $L$ in terms of the dimensions of certain boundary quotients of $L$ . This paper gives a purely frame-theoretic proof of this result, at once generalizing it to frames which are...

$G_{δ}$ -modification of compacta and cardinal invariants

Aleksander V. Arhangel'skii (2006)

Commentationes Mathematicae Universitatis Carolinae

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Given a space $X$ , its $G_{δ}$ -subsets form a basis of a new space $X_{ω}$ , called the $G_{δ}$ -modification of $X$ . We study how the assumption that the $G_{δ}$ -modification $X_{ω}$ is homogeneous influences properties of $X$ . If $X$ is first countable, then $X_{ω}$ is discrete and, hence, homogeneous. Thus, $X_{ω}$ is much more often homogeneous than $X$ itself. We prove that if $X$ is a compact Hausdorff space of countable tightness such that the $G_{δ}$ -modification of $X$ is homogeneous, then the weight $w (X)$ of $X$ does not exceed $2^{ω}$ (Theorem 1)....

Positive solutions for systems of generalized three-point nonlinear boundary value problems

Johnny Henderson, Sotiris K. Ntouyas, Ioannis K. Purnaras (2008)

Commentationes Mathematicae Universitatis Carolinae

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Values of $λ$ are determined for which there exist positive solutions of the system of three-point boundary value problems, $u^{''} + λ a (t) f (v) = 0$ , $v^{''} + λ b (t) g (u) = 0$ , for $0 < t < 1$ , and satisfying, $u (0) = β u (η)$ , $u (1) = α u (η)$ , $v (0) = β v (η)$ , $v (1) = α v (η)$ . A Guo-Krasnosel’skii fixed point theorem is applied.

A $β$ -normal Tychonoff space which is not normal

Eva Murtinová (2002)

Commentationes Mathematicae Universitatis Carolinae

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$α$ -normality and $β$ -normality are properties generalizing normality of topological spaces. They consist in separating dense subsets of closed disjoint sets. We construct an example of a Tychonoff $β$ -normal non-normal space and an example of a Hausdorff $α$ -normal non-regular space.

Displaying similar documents to “Existence results for a class of high order differential equation associated with integral boundary conditions at resonance”

Dimension in algebraic frames, II: Applications to frames of ideals in C ( X )

G δ -modification of compacta and cardinal invariants

Positive solutions for systems of generalized three-point nonlinear boundary value problems

A β -normal Tychonoff space which is not normal

Dimension in algebraic frames, II: Applications to frames of ideals in $C (X)$

$G_{δ}$ -modification of compacta and cardinal invariants

A $β$ -normal Tychonoff space which is not normal