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A nonlocal boundary value problem with singularities in phase variables
The singular differential equation (g(χ′))′ = ƒ(t, χ, χ′) together with the nonlocal boundary conditions χ(0) = χ(T) = −, γ min {χ(t) : t ∈ [0,T]} is considered. Here g ∈ C 0(ℝ) is an increasing and odd function, positive ƒ satisfying the local Carathéodory conditions on [0, T] × (ℝ s0}) su2 may be...
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| Published in: | Mathematical and computer modelling 2004-07, Vol.40 (1), p.101-116 |
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| Format: | Article |
| Language: | English |
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| cited_by | cdi_FETCH-LOGICAL-c399t-980397443d37bc3526f7394443586cb74fd8c09595734e6f9500a9c53f345afb3 |
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| cites | cdi_FETCH-LOGICAL-c399t-980397443d37bc3526f7394443586cb74fd8c09595734e6f9500a9c53f345afb3 |
| container_end_page | 116 |
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| container_start_page | 101 |
| container_title | Mathematical and computer modelling |
| container_volume | 40 |
| creator | STANEK, S |
| description | The singular differential equation
(g(χ′))′ = ƒ(t, χ, χ′) together with the nonlocal boundary conditions
χ(0) = χ(T) = −, γ min
{χ(t) : t ∈ [0,T]} is considered. Here
g ∈ C
0(ℝ)
is an increasing and odd function, positive ƒ satisfying the local Carathéodory conditions on
[0, T] × (ℝ s0})
su2 may be singular at the value 0 in all its phase variables and γ ∈ (o, ∞). The existence result for the above boundary value problem is proved by the regularization and sequential techniques. Proofs use the topological transversality principle and the Vitali's convergent theorem. |
| doi_str_mv | 10.1016/j.mcm.2003.11.003 |
| format | article |
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(g(χ′))′ = ƒ(t, χ, χ′) together with the nonlocal boundary conditions
χ(0) = χ(T) = −, γ min
{χ(t) : t ∈ [0,T]} is considered. Here
g ∈ C
0(ℝ)
is an increasing and odd function, positive ƒ satisfying the local Carathéodory conditions on
[0, T] × (ℝ s0})
su2 may be singular at the value 0 in all its phase variables and γ ∈ (o, ∞). The existence result for the above boundary value problem is proved by the regularization and sequential techniques. Proofs use the topological transversality principle and the Vitali's convergent theorem.</description><identifier>ISSN: 0895-7177</identifier><identifier>EISSN: 1872-9479</identifier><identifier>DOI: 10.1016/j.mcm.2003.11.003</identifier><language>eng</language><publisher>Oxford: Elsevier Ltd</publisher><subject>Exact sciences and technology ; Mathematical analysis ; Mathematics ; Methods of scientific computing (including symbolic computation, algebraic computation) ; Nonlocal boundary condition ; Numerical analysis. Scientific computation ; Ordinary differential equations ; Sciences and techniques of general use ; Second-order differential equation ; Singular boundary value problem ; Topological transversality principle ; Vitali's convergence theorem</subject><ispartof>Mathematical and computer modelling, 2004-07, Vol.40 (1), p.101-116</ispartof><rights>2004 Elsevier Ltd.</rights><rights>2004 INIST-CNRS</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c399t-980397443d37bc3526f7394443586cb74fd8c09595734e6f9500a9c53f345afb3</citedby><cites>FETCH-LOGICAL-c399t-980397443d37bc3526f7394443586cb74fd8c09595734e6f9500a9c53f345afb3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27924,27925</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=16115495$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>STANEK, S</creatorcontrib><title>A nonlocal boundary value problem with singularities in phase variables</title><title>Mathematical and computer modelling</title><description>The singular differential equation
(g(χ′))′ = ƒ(t, χ, χ′) together with the nonlocal boundary conditions
χ(0) = χ(T) = −, γ min
{χ(t) : t ∈ [0,T]} is considered. Here
g ∈ C
0(ℝ)
is an increasing and odd function, positive ƒ satisfying the local Carathéodory conditions on
[0, T] × (ℝ s0})
su2 may be singular at the value 0 in all its phase variables and γ ∈ (o, ∞). The existence result for the above boundary value problem is proved by the regularization and sequential techniques. Proofs use the topological transversality principle and the Vitali's convergent theorem.</description><subject>Exact sciences and technology</subject><subject>Mathematical analysis</subject><subject>Mathematics</subject><subject>Methods of scientific computing (including symbolic computation, algebraic computation)</subject><subject>Nonlocal boundary condition</subject><subject>Numerical analysis. Scientific computation</subject><subject>Ordinary differential equations</subject><subject>Sciences and techniques of general use</subject><subject>Second-order differential equation</subject><subject>Singular boundary value problem</subject><subject>Topological transversality principle</subject><subject>Vitali's convergence theorem</subject><issn>0895-7177</issn><issn>1872-9479</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2004</creationdate><recordtype>article</recordtype><recordid>eNp9kEFLAzEQhYMoWKs_wFsuets12SSbDZ5K0SoUvOg5ZLOJTclma7Jb8d-b0oI3Tw-G772ZeQDcYlRihOuHbdnrvqwQIiXGZZYzMMMNrwpBuTgHM9QIVnDM-SW4SmmLEGICNTOwWsAwBD9o5WE7TKFT8QfulZ8M3MWh9aaH327cwOTC5-RVdKMzCboAdxuVTCajU5lK1-DCKp_MzUnn4OP56X35UqzfVq_LxbrQRIixEA0iglNKOsJbTVhVW04EzQPW1Lrl1HaNRoIJxgk1tRUMISU0I5ZQpmxL5uD-mJuv-5pMGmXvkjbeq2CGKclKUEwbgjOIj6COQ0rRWLmLrs_fSYzkoTK5lbkyeahMYiyzZM_dKVylXIiNKmiX_ow1xowKlrnHI2fyp3tnokzamaBN56LRo-wG98-WX6PGgBA</recordid><startdate>20040701</startdate><enddate>20040701</enddate><creator>STANEK, S</creator><general>Elsevier Ltd</general><general>Elsevier Science</general><scope>6I.</scope><scope>AAFTH</scope><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20040701</creationdate><title>A nonlocal boundary value problem with singularities in phase variables</title><author>STANEK, S</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c399t-980397443d37bc3526f7394443586cb74fd8c09595734e6f9500a9c53f345afb3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2004</creationdate><topic>Exact sciences and technology</topic><topic>Mathematical analysis</topic><topic>Mathematics</topic><topic>Methods of scientific computing (including symbolic computation, algebraic computation)</topic><topic>Nonlocal boundary condition</topic><topic>Numerical analysis. Scientific computation</topic><topic>Ordinary differential equations</topic><topic>Sciences and techniques of general use</topic><topic>Second-order differential equation</topic><topic>Singular boundary value problem</topic><topic>Topological transversality principle</topic><topic>Vitali's convergence theorem</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>STANEK, S</creatorcontrib><collection>ScienceDirect Open Access Titles</collection><collection>Elsevier:ScienceDirect:Open Access</collection><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Mathematical and computer modelling</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>STANEK, S</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A nonlocal boundary value problem with singularities in phase variables</atitle><jtitle>Mathematical and computer modelling</jtitle><date>2004-07-01</date><risdate>2004</risdate><volume>40</volume><issue>1</issue><spage>101</spage><epage>116</epage><pages>101-116</pages><issn>0895-7177</issn><eissn>1872-9479</eissn><abstract>The singular differential equation
(g(χ′))′ = ƒ(t, χ, χ′) together with the nonlocal boundary conditions
χ(0) = χ(T) = −, γ min
{χ(t) : t ∈ [0,T]} is considered. Here
g ∈ C
0(ℝ)
is an increasing and odd function, positive ƒ satisfying the local Carathéodory conditions on
[0, T] × (ℝ s0})
su2 may be singular at the value 0 in all its phase variables and γ ∈ (o, ∞). The existence result for the above boundary value problem is proved by the regularization and sequential techniques. Proofs use the topological transversality principle and the Vitali's convergent theorem.</abstract><cop>Oxford</cop><pub>Elsevier Ltd</pub><doi>10.1016/j.mcm.2003.11.003</doi><tpages>16</tpages><oa>free_for_read</oa></addata></record> |
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| identifier | ISSN: 0895-7177 |
| ispartof | Mathematical and computer modelling, 2004-07, Vol.40 (1), p.101-116 |
| issn | 0895-7177 1872-9479 |
| language | eng |
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| source | ScienceDirect Freedom Collection |
| subjects | Exact sciences and technology Mathematical analysis Mathematics Methods of scientific computing (including symbolic computation, algebraic computation) Nonlocal boundary condition Numerical analysis. Scientific computation Ordinary differential equations Sciences and techniques of general use Second-order differential equation Singular boundary value problem Topological transversality principle Vitali's convergence theorem |
| title | A nonlocal boundary value problem with singularities in phase variables |
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