Temat: bifurcation - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: Nonlinear eigenvalue problems for fourth order ordinary differential equations
Autorzy:: Przybycin, Jolanta
Powiązania:: https://bibliotekanauki.pl/articles/1311640.pdf
Data publikacji:: 1995
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:: bifurcation point
bifurcation interval
Leray-Schauder degree
characteristic value
Opis:: This paper was inspired by the works of Chiappinelli ([3]) and Schmitt and Smith ([7]). We study the problem ℒu = λau + f(·,u,u',u'',u''') with separated boundary conditions on [0,π], where ℒ is a composition of two operators of Sturm-Liouville type. We assume that the nonlinear perturbation f satisfies the inequality |f(x,u,u',u'',u''')| ≤ M|u|. Because of the presence of f the considered equation does not in general have a linearization about 0. For this reason the global bifurcation theorem of Rabinowitz ([5], [6]) is not applicable here. We use the properties of Leray-Schauder degree to establish the existence of nontrivial solutions and describe their location. The results obtained are similar to those proved by Chiappinelli for Sturm-Liouville operators.
Źródło:: Annales Polonici Mathematici; 1994-1995, 60, 3; 249-253
0066-2216
Pojawia się w:: Annales Polonici Mathematici
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 2.

Tytuł:: Versal deformations of $D_q$-invariant 2-parameter families of planar vector fields
Autorzy:: Świrszcz, Grzegorz
Powiązania:: https://bibliotekanauki.pl/articles/1311417.pdf
Data publikacji:: 1995
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:: versal family
bifurcation
$D_q$-invariant
Opis:: The paper deals with 2-parameter families of planar vector fields which are invariant under the group $D_q$ for q ≥ 3. The germs at z = 0 of such families are studied and versal families are found. We also give the phase portraits of the versal families.
Źródło:: Annales Polonici Mathematici; 1995, 62, 3; 265-281
0066-2216
Pojawia się w:: Annales Polonici Mathematici
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 3.

Tytuł:: Generic saddle-node bifurcation for cascade second order ODEs on manifolds
Autorzy:: Medveď, Milan
Powiązania:: https://bibliotekanauki.pl/articles/1294406.pdf
Data publikacji:: 1998
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:: cascade
ODE
critical element
transversal
bifurcation
Opis:: Cascade second order ODEs on manifolds are defined. These objects are locally represented by coupled second order ODEs such that any solution of one of them can represent an external force for the other one. A generic saddle-node bifurcation theorem for 1-parameter families of cascade second order ODEs is proved.
Źródło:: Annales Polonici Mathematici; 1998, 68, 3; 211-225
0066-2216
Pojawia się w:: Annales Polonici Mathematici
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 4.

Tytuł:: Valeurs critiques asymptotiques dune fonction définissable dans une structure o-minimale
Autorzy:: D'Acunto, D.
Powiązania:: https://bibliotekanauki.pl/articles/1207923.pdf
Data publikacji:: 2000
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:: bifurcation set
asymptotic critical value
o-minimal structure
Opis:: We prove that the set of asymptotic critical values of a $C^1$ function definable in an o-minimal structure is finite, even if the structure is not polynomially bounded. As a consequence, the function is a locally trivial fibration over the complement of this set.
Źródło:: Annales Polonici Mathematici; 2000, 75, 1; 35-45
0066-2216
Pojawia się w:: Annales Polonici Mathematici
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 5.

Tytuł:: Bifurcation theorems of Rabinowitz type for certain differential operators of the fourth order
Autorzy:: Przybycin, Jolanta
Powiązania:: https://bibliotekanauki.pl/articles/1312084.pdf
Data publikacji:: 1992
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:: nonlinear partial differential equations
bifurcation in partial differential equations
Opis:: This paper was inspired by the works of P. H. Rabinowitz. We study nonlinear eigenvalue problems for some fourth order elliptic partial differential equations with nonlinear perturbation of Rabinowitz type. We show the existence of an unbounded continuum of nontrivial positive solutions bifurcating from (μ₁,0), where μ₁ is the first eigenvalue of the linearization about 0 of the considered problem. We also prove the related theorem for bifurcation from infinity. The results obtained are similar to those proved by Rabinowitz for second order elliptic partial differential equations ([5]-[7]). The methods used are based, in principle, on the results of [1], [5], [6].
Źródło:: Annales Polonici Mathematici; 1992, 57, 1; 21-28
0066-2216
Pojawia się w:: Annales Polonici Mathematici
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 6.

Tytuł:: On bifurcation intervals for nonlinear eigenvalue problems
Autorzy:: Przybycin, Jolanta
Powiązania:: https://bibliotekanauki.pl/articles/1294164.pdf
Data publikacji:: 1999
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:: bifurcation interval
symmetric operator
Sturm-Liouville problem
Dirichlet problem
Leray-Schauder degree
characteristic values
Opis:: We give a sufficient condition for [μ-M, μ+M] × {0} to be a bifurcation interval of the equation u = L(λu + F(u)), where L is a linear symmetric operator in a Hilbert space, μ ∈ r(L) is of odd multiplicity, and F is a nonlinear operator. This abstract result provides an elementary proof of the existence of bifurcation intervals for some eigenvalue problems with nondifferentiable nonlinearities. All the results obtained may be easily transferred to the case of bifurcation from infinity.
Źródło:: Annales Polonici Mathematici; 1999, 71, 1; 39-46
0066-2216
Pojawia się w:: Annales Polonici Mathematici
Dostawca treści:: Biblioteka Nauki

Artykuł

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