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In this paper, the existence and the localization result will be proven for vector Dirichlet problem with an upper-Carathéodory right-hand side. The result will be obtained by combining the continuation principle with bound sets technique.

A boundary value problem arising in the flow of a viscous fluid

Lee, Tai-Chi (1978)

Portugaliae mathematica

A boundary value problem for non-linear differential equations with a retarded argument

Józef Wenety Myjak (1973)

Annales Polonici Mathematici

A boundary value problem of fractional order at resonance.

Kosmatov, Nickolai (2010)

Electronic Journal of Differential Equations (EJDE) [electronic only]

A branching method for studying stability of a solution to a delay differential equation.

Dolgii, Yu.F., Nidchenko, S.N. (2005)

Sibirskij Matematicheskij Zhurnal

A. C. Clarke's Space Odyssey and Newton's law of gravity

Bartoň, Stanislav, Renčín, Lukáš (2017)

Programs and Algorithms of Numerical Mathematics

In his famous tetralogy, Space Odyssey, A. C. Clarke called the calculation of a motion of a mass point in the gravitational field of the massive cuboid a classical problem of gravitational mechanics. This article presents a proposal for a solution to this problem in terms of Newton's theory of gravity. First we discuss and generalize Newton's law of gravitation. We then compare the gravitational field created by the cuboid -- monolith, with the gravitational field of the homogeneous sphere. This...

A cantilever equation with nonlinear boundary conditions.

Infante, G., Pietramala, P. (2009)

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

A C...-Collocation-like Method for Two-Point Boundary Value Problems.

Zbigniew Leyk (1986)

Numerische Mathematik

A certain type of partial differential equations on tori

Michal Fečkan (1992)

Mathematica Bohemica

The existence of classical solutions for some partial differential equations on tori is shown.

A characterization of evolution operators

Naoki Tanaka (2001)

Studia Mathematica

A class of evolution operators is introduced according to the device of Kato. An evolution operator introduced here provides a classical solution of the linear equation u'(t) = A(t)u(t) for t ∈ [0,T], in a general Banach space. The paper presents a necessary and sufficient condition for the existence and uniqueness of such an evolution operator.

A characterization of isochronous centres in terms of symmetries.

Emilio Freire, Gasull, Armengol, Guillamon, Antoni 2 (2004)

Revista Matemática Iberoamericana

We present a description of isochronous centres of planar vector fields X by means of their groups of symmetries. More precisely, given a normalizer U of X (i.e., [X,U]= µ X, where µ is a scalar function), we provide a necessary and sufficient isochronicity condition based on µ. This criterion extends the result of Sabatini and Villarini that establishes the equivalence between isochronicity and the existence of commutators ([X,U]= 0). We put also special emphasis on the mechanical aspects of isochronicity;...

A characterization of the existence of solutions to some higher order boundary value problems

Gabriele Bonanno, Salvatore A. Marano (1995)

Commentationes Mathematicae Universitatis Carolinae

The aim of this short note is to present a theorem that characterizes the existence of solutions to a class of higher order boundary value problems. This result completely answers a question previously set by the authors in [Differential Integral Equations 6 (1993), 1119–1123].

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1D dirac operators with special periodic potentials

2 - kratnaya polnota sistemy sobstvennyh i prisoedinennyh funkcij differencial’nogo operatora $L_{2} (λ)$

A- and B-Stability for Runge-Kutta Methods - Characterizations and Equivalence.

A barrier method for quasilinear ordinary differential equations of the curvature type

A bifurcation result for Sturm-Liouville problems with a set-valued term.

A bound sets technique for Dirichlet problem with an upper-Carathéodory right-hand side