Displaying similar documents to “Bound sets and two-point boundary value problems for second order differential systems”

Boundary value problems for nonlinear perturbations of some ϕ-Laplacians

J. Mawhin (2007)

Banach Center Publications

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This paper surveys a number of recent results obtained by C. Bereanu and the author in existence results for second order differential equations of the form (ϕ(u'))' = f(t,u,u') submitted to various boundary conditions. In the equation, ϕ: ℝ → ≤ ]-a,a[ is a homeomorphism such that ϕ(0) = 0. An important motivation is the case of the curvature operator, where ϕ(s) = s/√(1+s²). The problems are reduced to fixed point problems in suitable function space,...

Nonlinear systems with mean curvature-like operators

Pierluigi Benevieri, João Marcos do Ó, Everaldo Souto de Medeiros (2007)

Banach Center Publications

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We give an existence result for a periodic boundary value problem involving mean curvature-like operators. Following a recent work of R. Manásevich and J. Mawhin, we use an approach based on the Leray-Schauder degree.

Curvature bounds for neighborhoods of self-similar sets

Steffen Winter (2011)

Commentationes Mathematicae Universitatis Carolinae

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In some recent work, fractal curvatures C k f ( F ) and fractal curvature measures C k f ( F , · ) , k = 0 , ... , d , have been determined for all self-similar sets F in ℝ d , for which the parallel neighborhoods satisfy a certain regularity condition and a certain rather technical curvature bound. The regularity condition is conjectured to be always satisfied, while the curvature bound has recently been shown to fail in some concrete examples. As a step towards a better understanding of its meaning, we discuss several equivalent...