Dirichlet problem with Φ-Laplacian and mixed singularities

Dirichlet problem with Φ-Laplacian and mixed singularities

We assume that A₁, A₂ ⊂ R are closed intervals containing 0, ϕ is an increasing odd homeomorphism with ϕ(R) = R and T ∈ (0,∞). We will study the singular Dirichlet problem of the form (ϕ(u' ))] + f(t, u, u' ) = 0 , u(0) = u(T) = 0, and we will prove the existence of its smooth solution sat...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Datum:2008
Hauptverfasser: Rachůnková, I., Stryja, J.
Format: Artikel
Sprache:English
Veröffentlicht: Інститут математики НАН України 2008
Schriftenreihe:Нелінійні коливання
Online Zugang:http://dspace.nbuv.gov.ua/handle/123456789/178150
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Zitieren:Dirichlet problem with Φ-Laplacian and mixed singularities / I. Rachůnková, J. Stryja // Нелінійні коливання. — 2008. — Т. 11, № 1. — С. 81-95. — Бібліогр.: 9 назв. — англ.

Institution

Digital Library of Periodicals of National Academy of Sciences of Ukraine
id irk-123456789-178150
record_format dspace
fulltext
spelling irk-123456789-1781502021-02-20T01:27:02Z Dirichlet problem with Φ-Laplacian and mixed singularities Rachůnková, I. Stryja, J. We assume that A₁, A₂ ⊂ R are closed intervals containing 0, ϕ is an increasing odd homeomorphism with ϕ(R) = R and T ∈ (0,∞). We will study the singular Dirichlet problem of the form (ϕ(u' ))] + f(t, u, u' ) = 0 , u(0) = u(T) = 0, and we will prove the existence of its smooth solution satisfying u(t) ∈ A₁ , u'(t) ∈ A₂ for t ∈ [0, T]. Here f satisfies the Caratheodory conditions on the set (0, T) × D and can have time singularities at t = 0, t = T and space singularities at x = 0, y = 0 Для замкнених iнтервалiв A₁, A₂ ⊂ R, якi мiстять 0, та зростаючого непарного гомеоморфiзму ϕ, який задовольняє умови ϕ(R) = R i T ∈ (0,∞), вивчено сингулярну задачу Дiрiхле вигляду (ϕ(u'))' + f(t, u, u' ) = 0 , u(0) = u(T) = 0, i доведено iснування гладкого розв’язку, що задовольняє умови u(t) ∈ A₁ , u'(t) ∈ A₂ для t ∈ [0, T]. Тут f задовольняє умови Каратеодорi на множинi (0, T) × D i може мати особливостi в t = 0, t = T та просторовi особливостi в x = 0, y = 0. 2008 Article Dirichlet problem with Φ-Laplacian and mixed singularities / I. Rachůnková, J. Stryja // Нелінійні коливання. — 2008. — Т. 11, № 1. — С. 81-95. — Бібліогр.: 9 назв. — англ. 1562-3076 http://dspace.nbuv.gov.ua/handle/123456789/178150 517.9 en Нелінійні коливання Інститут математики НАН України
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
language English
description We assume that A₁, A₂ ⊂ R are closed intervals containing 0, ϕ is an increasing odd homeomorphism with ϕ(R) = R and T ∈ (0,∞). We will study the singular Dirichlet problem of the form (ϕ(u' ))] + f(t, u, u' ) = 0 , u(0) = u(T) = 0, and we will prove the existence of its smooth solution satisfying u(t) ∈ A₁ , u'(t) ∈ A₂ for t ∈ [0, T]. Here f satisfies the Caratheodory conditions on the set (0, T) × D and can have time singularities at t = 0, t = T and space singularities at x = 0, y = 0
format Article
author Rachůnková, I.
Stryja, J.
spellingShingle Rachůnková, I.
Stryja, J.
Dirichlet problem with Φ-Laplacian and mixed singularities
Нелінійні коливання
author_facet Rachůnková, I.
Stryja, J.
author_sort Rachůnková, I.
title Dirichlet problem with Φ-Laplacian and mixed singularities
title_short Dirichlet problem with Φ-Laplacian and mixed singularities
title_full Dirichlet problem with Φ-Laplacian and mixed singularities
title_fullStr Dirichlet problem with Φ-Laplacian and mixed singularities
title_full_unstemmed Dirichlet problem with Φ-Laplacian and mixed singularities
title_sort dirichlet problem with φ-laplacian and mixed singularities
publisher Інститут математики НАН України
publishDate 2008
url http://dspace.nbuv.gov.ua/handle/123456789/178150
citation_txt Dirichlet problem with Φ-Laplacian and mixed singularities / I. Rachůnková, J. Stryja // Нелінійні коливання. — 2008. — Т. 11, № 1. — С. 81-95. — Бібліогр.: 9 назв. — англ.
series Нелінійні коливання
work_keys_str_mv AT rachunkovai dirichletproblemwithphlaplacianandmixedsingularities
AT stryjaj dirichletproblemwithphlaplacianandmixedsingularities
first_indexed 2025-07-15T16:31:00Z
last_indexed 2025-07-15T16:31:00Z
_version_ 1837731215939993600

Ähnliche Einträge