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Computing the differential of an unfolded contact diffeomorphism

Klaus Böhmer, Drahoslava Janovská, Vladimír Janovský (2003)

Applications of Mathematics

Consider a bifurcation problem, namely, its bifurcation equation. There is a diffeomorphism Φ linking the actual solution set with an unfolded normal form of the bifurcation equation. The differential D Φ ( 0 ) of this diffeomorphism is a valuable information for a numerical analysis of the imperfect bifurcation. The aim of this paper is to construct algorithms for a computation of D Φ ( 0 ) . Singularity classes containing bifurcation points with c o d i m 3 , c o r a n k = 1 are considered.

Conditional differential equations

Celina Rom (2016)

Applicationes Mathematicae

We introduce and study conditional differential equations, a kind of random differential equations. We give necessary and sufficient conditions for the existence of a solution of such an equation. We apply our main result to a Malthus type model.

Conditional oscillation of half-linear differential equations with periodic coefficients

Petr Hasil (2008)

Archivum Mathematicum

We show that the half-linear differential equation [ r ( t ) Φ ( x ' ) ] ' + s ( t ) t p Φ ( x ) = 0 * with α -periodic positive functions r , s is conditionally oscillatory, i.e., there exists a constant K > 0 such that () with γ s ( t ) t p instead of s ( t ) t p is oscillatory for γ > K and nonoscillatory for γ < K .

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