FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W3157147859> ?p ?o ?g. }

• W3157147859 endingPage "5209" @default.
• W3157147859 startingPage "5209" @default.
• W3157147859 abstract "<p style='text-indent:20px;'>We consider the following nonlocal critical equation</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id=FE145> begin{document}$begin{equation} -Delta u = (I_{mu_1}ast|u|^{2_{mu_1}^ast})|u|^{2_{mu_1}^ast-2}u +(I_{mu_2}ast|u|^{2_{mu_2}^ast})|u|^{2_{mu_2}^ast-2}u,; xinmathbb{R}^N, ;;;;;;;(1) end{equation}$ end{document} </tex-math></disp-formula></p><p style='text-indent:20px;'>where <inline-formula><tex-math id=M1>begin{document}$ 0&lt;mu_1,mu_2&lt;N $end{document}</tex-math></inline-formula> if <inline-formula><tex-math id=M2>begin{document}$ N = 3 $end{document}</tex-math></inline-formula> or <inline-formula><tex-math id=M3>begin{document}$ 4 $end{document}</tex-math></inline-formula>, and <inline-formula><tex-math id=M4>begin{document}$ N-4leqmu_1,mu_2&lt;N $end{document}</tex-math></inline-formula> if <inline-formula><tex-math id=M5>begin{document}$ Ngeq5 $end{document}</tex-math></inline-formula>, <inline-formula><tex-math id=M6>begin{document}$ 2_{mu_{i}}^ast: = frac{N+mu_i}{N-2}(i = 1,2) $end{document}</tex-math></inline-formula> is the upper critical exponent with respect to the Hardy-Littlewood-Sobolev inequality, and <inline-formula><tex-math id=M7>begin{document}$ I_{mu_i} $end{document}</tex-math></inline-formula> is the Riesz potential</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id=FE1> begin{document}$ begin{equation*} I_{mu_i}(x) = frac{Gamma(frac{N-mu_i}{2})}{Gamma(frac{mu_i}{2})pi^{frac{N}{2}}2^{mu_i}|x|^{N-mu_i}}, ; i = 1,2, end{equation*} $end{document} </tex-math></disp-formula></p><p style='text-indent:20px;'>with <inline-formula><tex-math id=M8>begin{document}$ Gamma(s) = int_{0}^{infty}x^{s-1}e^{-x}dx $end{document}</tex-math></inline-formula>, <inline-formula><tex-math id=M9>begin{document}$ s&gt;0 $end{document}</tex-math></inline-formula>. Firstly, we prove the existence of the solutions of the equation (1). We also establish integrability and <inline-formula><tex-math id=M10>begin{document}$ C^infty $end{document}</tex-math></inline-formula>-regularity of solutions and obtain the explicit forms of positive solutions via the method of moving spheres in integral forms. Finally, we show that the nondegeneracy of the linearized equation of (1) at <inline-formula><tex-math id=M11>begin{document}$ U_0,V_0 $end{document}</tex-math></inline-formula> when <inline-formula><tex-math id=M12>begin{document}$ max{mu_1,mu_2}rightarrow0 $end{document}</tex-math></inline-formula> and <inline-formula><tex-math id=M13>begin{document}$ min{mu_1,mu_2}rightarrow N $end{document}</tex-math></inline-formula>, respectively.</p>" @default.
• W3157147859 created "2021-05-10" @default.
• W3157147859 creator A5035716717 @default.
• W3157147859 creator A5046001568 @default.
• W3157147859 creator A5077128420 @default.
• W3157147859 date "2021-01-01" @default.
• W3157147859 modified "2023-10-12" @default.
• W3157147859 title "Classification of solutions to a nonlocal equation with doubly Hardy-Littlewood-Sobolev critical exponents" @default.
• W3157147859 cites W1659004305 @default.
• W3157147859 cites W1949063937 @default.
• W3157147859 cites W1965494863 @default.
• W3157147859 cites W1977212986 @default.
• W3157147859 cites W1982931837 @default.
• W3157147859 cites W1993604235 @default.
• W3157147859 cites W1994134181 @default.
• W3157147859 cites W1999794047 @default.
• W3157147859 cites W2007780149 @default.
• W3157147859 cites W2011667189 @default.
• W3157147859 cites W2011829237 @default.
• W3157147859 cites W2016670537 @default.
• W3157147859 cites W2017437908 @default.
• W3157147859 cites W2024191084 @default.
• W3157147859 cites W2032721195 @default.
• W3157147859 cites W2036340268 @default.
• W3157147859 cites W2040320111 @default.
• W3157147859 cites W2048272992 @default.
• W3157147859 cites W2051449318 @default.
• W3157147859 cites W2073460085 @default.
• W3157147859 cites W2075709627 @default.
• W3157147859 cites W2087613667 @default.
• W3157147859 cites W2088703745 @default.
• W3157147859 cites W2097775664 @default.
• W3157147859 cites W2107784368 @default.
• W3157147859 cites W2115353264 @default.
• W3157147859 cites W2325412313 @default.
• W3157147859 cites W2471102904 @default.
• W3157147859 cites W2562566872 @default.
• W3157147859 cites W2783496655 @default.
• W3157147859 cites W2795418500 @default.
• W3157147859 cites W2958134704 @default.
• W3157147859 cites W2962974112 @default.
• W3157147859 cites W2963931177 @default.
• W3157147859 cites W2964195781 @default.
• W3157147859 cites W3010866939 @default.
• W3157147859 cites W3027451051 @default.
• W3157147859 cites W3046974905 @default.
• W3157147859 cites W3094569562 @default.
• W3157147859 cites W3104068651 @default.
• W3157147859 cites W3138311438 @default.
• W3157147859 cites W4235609472 @default.
• W3157147859 cites W4236052448 @default.
• W3157147859 cites W4240704356 @default.
• W3157147859 cites W4248798422 @default.
• W3157147859 cites W4292081050 @default.
• W3157147859 doi "https://doi.org/10.3934/dcds.2021074" @default.
• W3157147859 hasPublicationYear "2021" @default.
• W3157147859 type Work @default.
• W3157147859 sameAs 3157147859 @default.
• W3157147859 citedByCount "9" @default.
• W3157147859 countsByYear W31571478592021 @default.
• W3157147859 countsByYear W31571478592022 @default.
• W3157147859 countsByYear W31571478592023 @default.
• W3157147859 crossrefType "journal-article" @default.
• W3157147859 hasAuthorship W3157147859A5035716717 @default.
• W3157147859 hasAuthorship W3157147859A5046001568 @default.
• W3157147859 hasAuthorship W3157147859A5077128420 @default.
• W3157147859 hasBestOaLocation W31571478591 @default.
• W3157147859 hasConcept C114614502 @default.
• W3157147859 hasConcept C121332964 @default.
• W3157147859 hasConcept C33923547 @default.
• W3157147859 hasConcept C94375191 @default.
• W3157147859 hasConceptScore W3157147859C114614502 @default.
• W3157147859 hasConceptScore W3157147859C121332964 @default.
• W3157147859 hasConceptScore W3157147859C33923547 @default.
• W3157147859 hasConceptScore W3157147859C94375191 @default.
• W3157147859 hasIssue "11" @default.
• W3157147859 hasLocation W31571478591 @default.
• W3157147859 hasOpenAccess W3157147859 @default.
• W3157147859 hasPrimaryLocation W31571478591 @default.
• W3157147859 hasRelatedWork W1978042415 @default.
• W3157147859 hasRelatedWork W2017331178 @default.
• W3157147859 hasRelatedWork W2135173043 @default.
• W3157147859 hasRelatedWork W2260035625 @default.
• W3157147859 hasRelatedWork W2319007069 @default.
• W3157147859 hasRelatedWork W2335699373 @default.
• W3157147859 hasRelatedWork W2963339245 @default.
• W3157147859 hasRelatedWork W2964072617 @default.
• W3157147859 hasRelatedWork W2976797620 @default.
• W3157147859 hasRelatedWork W4253321761 @default.
• W3157147859 hasVolume "41" @default.
• W3157147859 isParatext "false" @default.
• W3157147859 isRetracted "false" @default.
• W3157147859 magId "3157147859" @default.
• W3157147859 workType "article" @default.