FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W2091208307> ?p ?o ?g. }

• W2091208307 endingPage "791" @default.
• W2091208307 startingPage "775" @default.
• W2091208307 abstract "We study the existence of positive nonradial solutions of equation <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=normal upper Delta u plus f left-parenthesis u right-parenthesis equals 0> <mml:semantics> <mml:mrow> <mml:mi mathvariant=normal>Δ<!-- Δ --></mml:mi> <mml:mi>u</mml:mi> <mml:mo>+</mml:mo> <mml:mi>f</mml:mi> <mml:mo stretchy=false>(</mml:mo> <mml:mi>u</mml:mi> <mml:mo stretchy=false>)</mml:mo> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> <mml:annotation encoding=application/x-tex>Delta u + f(u) = 0</mml:annotation> </mml:semantics> </mml:math> </inline-formula> in <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=normal upper Omega Subscript a> <mml:semantics> <mml:mrow class=MJX-TeXAtom-ORD> <mml:msub> <mml:mi mathvariant=normal>Ω<!-- Ω --></mml:mi> <mml:mi>a</mml:mi> </mml:msub> </mml:mrow> <mml:annotation encoding=application/x-tex>{Omega _a}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=u equals 0> <mml:semantics> <mml:mrow> <mml:mi>u</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> <mml:annotation encoding=application/x-tex>u = 0</mml:annotation> </mml:semantics> </mml:math> </inline-formula> on <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=partial-differential normal upper Omega Subscript a> <mml:semantics> <mml:mrow> <mml:mi mathvariant=normal>∂<!-- ∂ --></mml:mi> <mml:mrow class=MJX-TeXAtom-ORD> <mml:msub> <mml:mi mathvariant=normal>Ω<!-- Ω --></mml:mi> <mml:mi>a</mml:mi> </mml:msub> </mml:mrow> </mml:mrow> <mml:annotation encoding=application/x-tex>partial {Omega _a}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, where <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=normal upper Omega Subscript a Baseline equals StartSet x element-of double-struck upper R Superscript n Baseline colon a greater-than StartAbsoluteValue x EndAbsoluteValue greater-than 1 EndSet> <mml:semantics> <mml:mrow> <mml:mrow class=MJX-TeXAtom-ORD> <mml:msub> <mml:mi mathvariant=normal>Ω<!-- Ω --></mml:mi> <mml:mi>a</mml:mi> </mml:msub> </mml:mrow> <mml:mo>=</mml:mo> <mml:mo fence=false stretchy=false>{</mml:mo> <mml:mi>x</mml:mi> <mml:mo>∈<!-- ∈ --></mml:mo> <mml:mrow class=MJX-TeXAtom-ORD> <mml:msup> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=double-struck>R</mml:mi> </mml:mrow> <mml:mi>n</mml:mi> </mml:msup> </mml:mrow> <mml:mo>:</mml:mo> <mml:mi>a</mml:mi> <mml:mo>></mml:mo> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mo stretchy=false>|</mml:mo> </mml:mrow> <mml:mi>x</mml:mi> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mo stretchy=false>|</mml:mo> </mml:mrow> <mml:mo>></mml:mo> <mml:mn>1</mml:mn> <mml:mo fence=false stretchy=false>}</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>{Omega _a} = { x in {mathbb {R}^n}:a > |x| > 1}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is an annulus in <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=double-struck upper R Superscript n> <mml:semantics> <mml:mrow class=MJX-TeXAtom-ORD> <mml:msup> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=double-struck>R</mml:mi> </mml:mrow> <mml:mi>n</mml:mi> </mml:msup> </mml:mrow> <mml:annotation encoding=application/x-tex>{mathbb {R}^n}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=n greater-than-or-equal-to 2> <mml:semantics> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>≥<!-- ≥ --></mml:mo> <mml:mn>2</mml:mn> </mml:mrow> <mml:annotation encoding=application/x-tex>n geq 2</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, and <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=f> <mml:semantics> <mml:mi>f</mml:mi> <mml:annotation encoding=application/x-tex>f</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is positive and superlinear at both <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=0> <mml:semantics> <mml:mn>0</mml:mn> <mml:annotation encoding=application/x-tex>0</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=normal infinity> <mml:semantics> <mml:mi mathvariant=normal>∞<!-- ∞ --></mml:mi> <mml:annotation encoding=application/x-tex>infty</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. We use a bifurcation method to show that there is a nonradial bifurcation with mode <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=k> <mml:semantics> <mml:mi>k</mml:mi> <mml:annotation encoding=application/x-tex>k</mml:annotation> </mml:semantics> </mml:math> </inline-formula> at <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=a Subscript k Baseline element-of left-parenthesis 0 comma 1 right-parenthesis> <mml:semantics> <mml:mrow> <mml:mrow class=MJX-TeXAtom-ORD> <mml:msub> <mml:mi>a</mml:mi> <mml:mi>k</mml:mi> </mml:msub> </mml:mrow> <mml:mo>∈<!-- ∈ --></mml:mo> <mml:mo stretchy=false>(</mml:mo> <mml:mn>0</mml:mn> <mml:mo>,</mml:mo> <mml:mn>1</mml:mn> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>{a_k} in (0,1)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> for any positive integer <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=k> <mml:semantics> <mml:mi>k</mml:mi> <mml:annotation encoding=application/x-tex>k</mml:annotation> </mml:semantics> </mml:math> </inline-formula> if <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=f> <mml:semantics> <mml:mi>f</mml:mi> <mml:annotation encoding=application/x-tex>f</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is subcritical and for large <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=k> <mml:semantics> <mml:mi>k</mml:mi> <mml:annotation encoding=application/x-tex>k</mml:annotation> </mml:semantics> </mml:math> </inline-formula> if <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=f> <mml:semantics> <mml:mi>f</mml:mi> <mml:annotation encoding=application/x-tex>f</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is supercritical. When <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=f> <mml:semantics> <mml:mi>f</mml:mi> <mml:annotation encoding=application/x-tex>f</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is subcritical, then a Nehari-type variational method can be used to prove that there exists <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=a Superscript asterisk Baseline element-of left-parenthesis 0 comma 1 right-parenthesis> <mml:semantics> <mml:mrow> <mml:mrow class=MJX-TeXAtom-ORD> <mml:msup> <mml:mi>a</mml:mi> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mo>∗<!-- ∗ --></mml:mo> </mml:mrow> </mml:msup> </mml:mrow> <mml:mo>∈<!-- ∈ --></mml:mo> <mml:mo stretchy=false>(</mml:mo> <mml:mn>0</mml:mn> <mml:mo>,</mml:mo> <mml:mn>1</mml:mn> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>{a^{ast } } in (0,1)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> such that for any <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=a element-of left-parenthesis a Superscript asterisk Baseline comma 1 right-parenthesis> <mml:semantics> <mml:mrow> <mml:mi>a</mml:mi> <mml:mo>∈<!-- ∈ --></mml:mo> <mml:mo stretchy=false>(</mml:mo> <mml:mrow class=MJX-TeXAtom-ORD> <mml:msup> <mml:mi>a</mml:mi> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mo>∗<!-- ∗ --></mml:mo> </mml:mrow> </mml:msup> </mml:mrow> <mml:mo>,</mml:mo> <mml:mn>1</mml:mn> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>a in ({a^{ast } },1)</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, the equation has a nonradial solution on <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=normal upper Omega Subscript a> <mml:semantics> <mml:mrow class=MJX-TeXAtom-ORD> <mml:msub> <mml:mi mathvariant=normal>Ω<!-- Ω --></mml:mi> <mml:mi>a</mml:mi> </mml:msub> </mml:mrow> <mml:annotation encoding=application/x-tex>{Omega _a}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>." @default.
• W2091208307 created "2016-06-24" @default.
• W2091208307 creator A5066009311 @default.
• W2091208307 date "1992-01-01" @default.
• W2091208307 modified "2023-09-25" @default.
• W2091208307 title "Existence of positive nonradial solutions for nonlinear elliptic equations in annular domains" @default.
• W2091208307 cites W1535130726 @default.
• W2091208307 cites W1783593475 @default.
• W2091208307 cites W1965039382 @default.
• W2091208307 cites W1970169700 @default.
• W2091208307 cites W1973559315 @default.
• W2091208307 cites W1982357817 @default.
• W2091208307 cites W1982931837 @default.
• W2091208307 cites W1998576880 @default.
• W2091208307 cites W2037558777 @default.
• W2091208307 cites W2037911926 @default.
• W2091208307 cites W2038928461 @default.
• W2091208307 cites W2075975725 @default.
• W2091208307 cites W2077130143 @default.
• W2091208307 cites W2092717001 @default.
• W2091208307 cites W2093957401 @default.
• W2091208307 cites W2325412313 @default.
• W2091208307 cites W2414980330 @default.
• W2091208307 doi "https://doi.org/10.1090/s0002-9947-1992-1055571-1" @default.
• W2091208307 hasPublicationYear "1992" @default.
• W2091208307 type Work @default.
• W2091208307 sameAs 2091208307 @default.
• W2091208307 citedByCount "24" @default.
• W2091208307 countsByYear W20912083072012 @default.
• W2091208307 countsByYear W20912083072013 @default.
• W2091208307 countsByYear W20912083072014 @default.
• W2091208307 countsByYear W20912083072016 @default.
• W2091208307 countsByYear W20912083072017 @default.
• W2091208307 countsByYear W20912083072018 @default.
• W2091208307 countsByYear W20912083072019 @default.
• W2091208307 countsByYear W20912083072020 @default.
• W2091208307 countsByYear W20912083072021 @default.
• W2091208307 countsByYear W20912083072023 @default.
• W2091208307 crossrefType "journal-article" @default.
• W2091208307 hasAuthorship W2091208307A5066009311 @default.
• W2091208307 hasBestOaLocation W20912083071 @default.
• W2091208307 hasConcept C11413529 @default.
• W2091208307 hasConcept C154945302 @default.
• W2091208307 hasConcept C2776321320 @default.
• W2091208307 hasConcept C41008148 @default.
• W2091208307 hasConcept C77088390 @default.
• W2091208307 hasConceptScore W2091208307C11413529 @default.
• W2091208307 hasConceptScore W2091208307C154945302 @default.
• W2091208307 hasConceptScore W2091208307C2776321320 @default.
• W2091208307 hasConceptScore W2091208307C41008148 @default.
• W2091208307 hasConceptScore W2091208307C77088390 @default.
• W2091208307 hasIssue "2" @default.
• W2091208307 hasLocation W20912083071 @default.
• W2091208307 hasOpenAccess W2091208307 @default.
• W2091208307 hasPrimaryLocation W20912083071 @default.
• W2091208307 hasRelatedWork W151193258 @default.
• W2091208307 hasRelatedWork W1529400504 @default.
• W2091208307 hasRelatedWork W1871911958 @default.
• W2091208307 hasRelatedWork W1892467659 @default.
• W2091208307 hasRelatedWork W2348710178 @default.
• W2091208307 hasRelatedWork W2808586768 @default.
• W2091208307 hasRelatedWork W2998403542 @default.
• W2091208307 hasRelatedWork W3201926073 @default.
• W2091208307 hasRelatedWork W38394648 @default.
• W2091208307 hasRelatedWork W73525116 @default.
• W2091208307 hasVolume "332" @default.
• W2091208307 isParatext "false" @default.
• W2091208307 isRetracted "false" @default.
• W2091208307 magId "2091208307" @default.
• W2091208307 workType "article" @default.