Nonlinear spectral problem for a self-adjoint vector differential equation
We consider a spectral problem that is nonlinear in the spectral parameter for a self-adjoint vector differential equation of order 2 n . The boundary conditions depend on the spectral parameter and are self-adjoint as well. Under some conditions of monotonicity of the input data with respect to the...
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| Veröffentlicht in: | Differential equations 2017-07, Vol.53 (7), p.900-907 |
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| creator | Abramov, A. A. Yukhno, L. F. |
| description | We consider a spectral problem that is nonlinear in the spectral parameter for a self-adjoint vector differential equation of order 2
n
. The boundary conditions depend on the spectral parameter and are self-adjoint as well. Under some conditions of monotonicity of the input data with respect to the spectral parameter, we present a method for counting the eigenvalues of the problem in a given interval. If the boundary conditions are independent of the spectral parameter, then we define the notion of number of an eigenvalue and give a method for computing this number as well as the set of numbers of all eigenvalues in a given interval. For an equation considered on an unbounded interval, under some additional assumptions, we present a method for approximating the original singular problem by a problem on a finite interval. |
| doi_str_mv | 10.1134/S0012266117070060 |
| format | Article |
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n
. The boundary conditions depend on the spectral parameter and are self-adjoint as well. Under some conditions of monotonicity of the input data with respect to the spectral parameter, we present a method for counting the eigenvalues of the problem in a given interval. If the boundary conditions are independent of the spectral parameter, then we define the notion of number of an eigenvalue and give a method for computing this number as well as the set of numbers of all eigenvalues in a given interval. For an equation considered on an unbounded interval, under some additional assumptions, we present a method for approximating the original singular problem by a problem on a finite interval.</description><identifier>ISSN: 0012-2661</identifier><identifier>EISSN: 1608-3083</identifier><identifier>DOI: 10.1134/S0012266117070060</identifier><language>eng</language><publisher>Moscow: Pleiades Publishing</publisher><subject>Boundary conditions ; Difference and Functional Equations ; Differential equations ; Eigenvalues ; Mathematics ; Mathematics and Statistics ; Nonlinear systems ; Numerical Methods ; Ordinary Differential Equations ; Partial Differential Equations ; Spectra</subject><ispartof>Differential equations, 2017-07, Vol.53 (7), p.900-907</ispartof><rights>Pleiades Publishing, Ltd. 2017</rights><rights>Differential Equations is a copyright of Springer, 2017.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c268t-b4806e4fda53fdc3534423f0489d5e25ea9d3e302424596fe1bf32bb88cf48433</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1134/S0012266117070060$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1134/S0012266117070060$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>315,781,785,27929,27930,41493,42562,51324</link.rule.ids></links><search><creatorcontrib>Abramov, A. A.</creatorcontrib><creatorcontrib>Yukhno, L. F.</creatorcontrib><title>Nonlinear spectral problem for a self-adjoint vector differential equation</title><title>Differential equations</title><addtitle>Diff Equat</addtitle><description>We consider a spectral problem that is nonlinear in the spectral parameter for a self-adjoint vector differential equation of order 2
n
. The boundary conditions depend on the spectral parameter and are self-adjoint as well. Under some conditions of monotonicity of the input data with respect to the spectral parameter, we present a method for counting the eigenvalues of the problem in a given interval. If the boundary conditions are independent of the spectral parameter, then we define the notion of number of an eigenvalue and give a method for computing this number as well as the set of numbers of all eigenvalues in a given interval. 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A.</au><au>Yukhno, L. F.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Nonlinear spectral problem for a self-adjoint vector differential equation</atitle><jtitle>Differential equations</jtitle><stitle>Diff Equat</stitle><date>2017-07-01</date><risdate>2017</risdate><volume>53</volume><issue>7</issue><spage>900</spage><epage>907</epage><pages>900-907</pages><issn>0012-2661</issn><eissn>1608-3083</eissn><abstract>We consider a spectral problem that is nonlinear in the spectral parameter for a self-adjoint vector differential equation of order 2
n
. The boundary conditions depend on the spectral parameter and are self-adjoint as well. Under some conditions of monotonicity of the input data with respect to the spectral parameter, we present a method for counting the eigenvalues of the problem in a given interval. If the boundary conditions are independent of the spectral parameter, then we define the notion of number of an eigenvalue and give a method for computing this number as well as the set of numbers of all eigenvalues in a given interval. For an equation considered on an unbounded interval, under some additional assumptions, we present a method for approximating the original singular problem by a problem on a finite interval.</abstract><cop>Moscow</cop><pub>Pleiades Publishing</pub><doi>10.1134/S0012266117070060</doi><tpages>8</tpages></addata></record> |
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| source | SpringerNature Journals |
| subjects | Boundary conditions Difference and Functional Equations Differential equations Eigenvalues Mathematics Mathematics and Statistics Nonlinear systems Numerical Methods Ordinary Differential Equations Partial Differential Equations Spectra |
| title | Nonlinear spectral problem for a self-adjoint vector differential equation |
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