Displaying similar documents to “Localization of nonsmooth lower and upper functions for periodic boundary value problems”

Resonance and multiplicity in periodic boundary value problems with singularity

Irena Rachůnková, Milan Tvrdý, Ivo Vrkoč (2003)

Mathematica Bohemica

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The paper deals with the boundary value problem u ' ' + k u = g ( u ) + e ( t ) , u ( 0 ) = u ( 2 π ) , u ' ( 0 ) = u ' ( 2 π ) , where k ∈ ℝ , g I ↦ ℝ is continuous, e ∈ 𝕃 J and lim x → 0 + ∫ x 1 g ( s ) d s = ∞ . In particular, the existence and multiplicity results are obtained by using the method of lower and upper functions which are constructed as solutions of related auxiliary linear problems.

An almost-periodicity criterion for solutions of the oscillatory differential equation y ' ' = q ( t ) y and its applications

Staněk, Svatoslav (2005)

Archivum Mathematicum

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The linear differential equation ( q ) : y ' ' = q ( t ) y with the uniformly almost-periodic function q is considered. Necessary and sufficient conditions which guarantee that all bounded (on ℝ ) solutions of ( q ) are uniformly almost-periodic functions are presented. The conditions are stated by a phase of ( q ) . Next, a class of equations of the type ( q ) whose all non-trivial solutions are bounded and not uniformly almost-periodic is given. Finally, uniformly almost-periodic solutions of the non-homogeneous differential...