FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W2038295590> ?p ?o ?g. }

• W2038295590 endingPage "2365" @default.
• W2038295590 startingPage "2357" @default.
• W2038295590 abstract "Let <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper X> <mml:semantics> <mml:mi>X</mml:mi> <mml:annotation encoding=application/x-tex>X</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be a real separable Banach space. The boundary value problem <disp-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=StartLayout 1st Row with Label left-parenthesis upper B right-parenthesis EndLabel StartLayout 1st Row 1st Column Blank 2nd Column a m p semicolon x prime element-of upper A left-parenthesis t right-parenthesis x plus upper F left-parenthesis t comma x right-parenthesis comma t element-of script upper R Subscript plus Baseline comma 2nd Row 1st Column Blank 2nd Column a m p semicolon upper U x equals a comma EndLayout EndLayout> <mml:semantics> <mml:mtable side=left displaystyle=false> <mml:mlabeledtr> <mml:mtd> <mml:mtext>(B)</mml:mtext> </mml:mtd> <mml:mtd> <mml:mtable columnalign=right left rowspacing=3pt columnspacing=0em side=left displaystyle=true> <mml:mtr> <mml:mtd /> <mml:mtd> <mml:mi>a</mml:mi> <mml:mi>m</mml:mi> <mml:mi>p</mml:mi> <mml:mo>;</mml:mo> <mml:msup> <mml:mi>x</mml:mi> <mml:mo>′</mml:mo> </mml:msup> <mml:mo>∈<!-- ∈ --></mml:mo> <mml:mi>A</mml:mi> <mml:mo stretchy=false>(</mml:mo> <mml:mi>t</mml:mi> <mml:mo stretchy=false>)</mml:mo> <mml:mi>x</mml:mi> <mml:mo>+</mml:mo> <mml:mi>F</mml:mi> <mml:mo stretchy=false>(</mml:mo> <mml:mi>t</mml:mi> <mml:mo>,</mml:mo> <mml:mi>x</mml:mi> <mml:mo stretchy=false>)</mml:mo> <mml:mo>,</mml:mo> <mml:mtext> </mml:mtext> <mml:mi>t</mml:mi> <mml:mo>∈<!-- ∈ --></mml:mo> <mml:msub> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi class=MJX-tex-caligraphic mathvariant=script>R</mml:mi> </mml:mrow> <mml:mo>+</mml:mo> </mml:msub> <mml:mo>,</mml:mo> </mml:mtd> </mml:mtr> <mml:mtr> <mml:mtd /> <mml:mtd> <mml:mi>a</mml:mi> <mml:mi>m</mml:mi> <mml:mi>p</mml:mi> <mml:mo>;</mml:mo> <mml:mi>U</mml:mi> <mml:mi>x</mml:mi> <mml:mo>=</mml:mo> <mml:mi>a</mml:mi> <mml:mo>,</mml:mo> </mml:mtd> </mml:mtr> </mml:mtable> </mml:mtd> </mml:mlabeledtr> </mml:mtable> <mml:annotation encoding=application/x-tex>begin{equation*} begin {split} &x’ in A(t)x+F(t,x),~tin mathcal {R}_+, &Ux = a, end{split} tag *{(B)} end{equation*}</mml:annotation> </mml:semantics> </mml:math> </disp-formula> is studied on the infinite interval <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper R Subscript plus Baseline equals left-bracket 0 comma normal infinity right-parenthesis period> <mml:semantics> <mml:mrow> <mml:msub> <mml:mi>R</mml:mi> <mml:mo>+</mml:mo> </mml:msub> <mml:mo>=</mml:mo> <mml:mo stretchy=false>[</mml:mo> <mml:mn>0</mml:mn> <mml:mo>,</mml:mo> <mml:mi mathvariant=normal>∞<!-- ∞ --></mml:mi> <mml:mo stretchy=false>)</mml:mo> <mml:mo>.</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>R_+=[0,infty ).</mml:annotation> </mml:semantics> </mml:math> </inline-formula> Here, the closed and densely defined linear operator <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper A left-parenthesis t right-parenthesis colon upper X superset-of upper D left-parenthesis upper A right-parenthesis right-arrow upper X comma t element-of script upper R Subscript plus Baseline comma> <mml:semantics> <mml:mrow> <mml:mi>A</mml:mi> <mml:mo stretchy=false>(</mml:mo> <mml:mi>t</mml:mi> <mml:mo stretchy=false>)</mml:mo> <mml:mo>:</mml:mo> <mml:mi>X</mml:mi> <mml:mo>⊃<!-- ⊃ --></mml:mo> <mml:mi>D</mml:mi> <mml:mo stretchy=false>(</mml:mo> <mml:mi>A</mml:mi> <mml:mo stretchy=false>)</mml:mo> <mml:mo stretchy=false>→<!-- → --></mml:mo> <mml:mi>X</mml:mi> <mml:mo>,</mml:mo> <mml:mtext> </mml:mtext> <mml:mi>t</mml:mi> <mml:mo>∈<!-- ∈ --></mml:mo> <mml:msub> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi class=MJX-tex-caligraphic mathvariant=script>R</mml:mi> </mml:mrow> <mml:mo>+</mml:mo> </mml:msub> <mml:mo>,</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>A(t):Xsupset D(A)to X,~tin mathcal {R}_+,</mml:annotation> </mml:semantics> </mml:math> </inline-formula> generates an evolution operator <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper W left-parenthesis t comma s right-parenthesis period> <mml:semantics> <mml:mrow> <mml:mi>W</mml:mi> <mml:mo stretchy=false>(</mml:mo> <mml:mi>t</mml:mi> <mml:mo>,</mml:mo> <mml:mi>s</mml:mi> <mml:mo stretchy=false>)</mml:mo> <mml:mo>.</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>W(t,s).</mml:annotation> </mml:semantics> </mml:math> </inline-formula> The function <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper F colon script upper R Subscript plus Baseline times upper X right-arrow 2 Superscript upper X> <mml:semantics> <mml:mrow> <mml:mi>F</mml:mi> <mml:mo>:</mml:mo> <mml:msub> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi class=MJX-tex-caligraphic mathvariant=script>R</mml:mi> </mml:mrow> <mml:mo>+</mml:mo> </mml:msub> <mml:mo>×<!-- × --></mml:mo> <mml:mi>X</mml:mi> <mml:mo stretchy=false>→<!-- → --></mml:mo> <mml:msup> <mml:mn>2</mml:mn> <mml:mi>X</mml:mi> </mml:msup> </mml:mrow> <mml:annotation encoding=application/x-tex>F:mathcal {R}_+times Xto 2^X</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is measurable in its first variable, upper semicontinuous in its second and has weakly compact and convex values. Either <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper F> <mml:semantics> <mml:mi>F</mml:mi> <mml:annotation encoding=application/x-tex>F</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is bounded and <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper W left-parenthesis t comma s right-parenthesis> <mml:semantics> <mml:mrow> <mml:mi>W</mml:mi> <mml:mo stretchy=false>(</mml:mo> <mml:mi>t</mml:mi> <mml:mo>,</mml:mo> <mml:mi>s</mml:mi> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>W(t,s)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is compact for <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=t greater-than s comma> <mml:semantics> <mml:mrow> <mml:mi>t</mml:mi> <mml:mo>></mml:mo> <mml:mi>s</mml:mi> <mml:mo>,</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>t > s,</mml:annotation> </mml:semantics> </mml:math> </inline-formula> or <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper F> <mml:semantics> <mml:mi>F</mml:mi> <mml:annotation encoding=application/x-tex>F</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is compact and <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper W left-parenthesis t comma s right-parenthesis> <mml:semantics> <mml:mrow> <mml:mi>W</mml:mi> <mml:mo stretchy=false>(</mml:mo> <mml:mi>t</mml:mi> <mml:mo>,</mml:mo> <mml:mi>s</mml:mi> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>W(t,s)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is equicontinuous. The mapping <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper U colon upper C Subscript b Baseline left-parenthesis script upper R Subscript plus Baseline comma upper X right-parenthesis right-arrow upper X> <mml:semantics> <mml:mrow> <mml:mi>U</mml:mi> <mml:mo>:</mml:mo> <mml:msub> <mml:mi>C</mml:mi> <mml:mi>b</mml:mi> </mml:msub> <mml:mo stretchy=false>(</mml:mo> <mml:msub> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi class=MJX-tex-caligraphic mathvariant=script>R</mml:mi> </mml:mrow> <mml:mo>+</mml:mo> </mml:msub> <mml:mo>,</mml:mo> <mml:mi>X</mml:mi> <mml:mo stretchy=false>)</mml:mo> <mml:mo stretchy=false>→<!-- → --></mml:mo> <mml:mi>X</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>U:C_b(mathcal {R}_+,X)to X</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is a bounded linear operator and <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=a element-of upper X> <mml:semantics> <mml:mrow> <mml:mi>a</mml:mi> <mml:mo>∈<!-- ∈ --></mml:mo> <mml:mi>X</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>ain X</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is fixed. The nonresonance problem is solved by using Ma’s fixed point theorem along with a recent result of Przeradzki which characterizes the compact sets in <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper C Subscript b Baseline left-parenthesis script upper R Subscript plus Baseline comma upper X right-parenthesis period> <mml:semantics> <mml:mrow> <mml:msub> <mml:mi>C</mml:mi> <mml:mi>b</mml:mi> </mml:msub> <mml:mo stretchy=false>(</mml:mo> <mml:msub> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi class=MJX-tex-caligraphic mathvariant=script>R</mml:mi> </mml:mrow> <mml:mo>+</mml:mo> </mml:msub> <mml:mo>,</mml:mo> <mml:mi>X</mml:mi> <mml:mo stretchy=false>)</mml:mo> <mml:mo>.</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>C_b(mathcal {R}_+,X).</mml:annotation> </mml:semantics> </mml:math> </inline-formula>" @default.
• W2038295590 created "2016-06-24" @default.
• W2038295590 creator A5007437880 @default.
• W2038295590 creator A5060876724 @default.
• W2038295590 date "1996-01-01" @default.
• W2038295590 modified "2023-10-18" @default.
• W2038295590 title "Nonresonance problems for differential inclusions in separable Banach spaces" @default.
• W2038295590 cites W1988379628 @default.
• W2038295590 cites W2010545404 @default.
• W2038295590 cites W2012877496 @default.
• W2038295590 cites W2014234860 @default.
• W2038295590 cites W2026911011 @default.
• W2038295590 cites W2083666395 @default.
• W2038295590 cites W2102922757 @default.
• W2038295590 cites W2124994003 @default.
• W2038295590 cites W4210718478 @default.
• W2038295590 cites W4213346713 @default.
• W2038295590 cites W4249780711 @default.
• W2038295590 cites W772205185 @default.
• W2038295590 cites W2067271524 @default.
• W2038295590 doi "https://doi.org/10.1090/s0002-9939-96-03439-9" @default.
• W2038295590 hasPublicationYear "1996" @default.
• W2038295590 type Work @default.
• W2038295590 sameAs 2038295590 @default.
• W2038295590 citedByCount "10" @default.
• W2038295590 countsByYear W20382955902012 @default.
• W2038295590 countsByYear W20382955902018 @default.
• W2038295590 crossrefType "journal-article" @default.
• W2038295590 hasAuthorship W2038295590A5007437880 @default.
• W2038295590 hasAuthorship W2038295590A5060876724 @default.
• W2038295590 hasBestOaLocation W20382955901 @default.
• W2038295590 hasConcept C11413529 @default.
• W2038295590 hasConcept C134306372 @default.
• W2038295590 hasConcept C154945302 @default.
• W2038295590 hasConcept C33923547 @default.
• W2038295590 hasConcept C41008148 @default.
• W2038295590 hasConcept C70710897 @default.
• W2038295590 hasConceptScore W2038295590C11413529 @default.
• W2038295590 hasConceptScore W2038295590C134306372 @default.
• W2038295590 hasConceptScore W2038295590C154945302 @default.
• W2038295590 hasConceptScore W2038295590C33923547 @default.
• W2038295590 hasConceptScore W2038295590C41008148 @default.
• W2038295590 hasConceptScore W2038295590C70710897 @default.
• W2038295590 hasIssue "8" @default.
• W2038295590 hasLocation W20382955901 @default.
• W2038295590 hasOpenAccess W2038295590 @default.
• W2038295590 hasPrimaryLocation W20382955901 @default.
• W2038295590 hasRelatedWork W1580435510 @default.
• W2038295590 hasRelatedWork W1970101876 @default.
• W2038295590 hasRelatedWork W1971514761 @default.
• W2038295590 hasRelatedWork W1985684185 @default.
• W2038295590 hasRelatedWork W2081616371 @default.
• W2038295590 hasRelatedWork W2323168379 @default.
• W2038295590 hasRelatedWork W2323683917 @default.
• W2038295590 hasRelatedWork W2327171221 @default.
• W2038295590 hasRelatedWork W2963826957 @default.
• W2038295590 hasRelatedWork W3107474891 @default.
• W2038295590 hasVolume "124" @default.
• W2038295590 isParatext "false" @default.
• W2038295590 isRetracted "false" @default.
• W2038295590 magId "2038295590" @default.
• W2038295590 workType "article" @default.