Matches in SemOpenAlex for { <https://semopenalex.org/work/W3000992283> ?p ?o ?g. }
Showing items 1 to 77 of
77
with 100 items per page.
- W3000992283 abstract "Abstract We are concerned with a nonnegative solution to the scalar field equation $$Delta u + f(u) = 0{rm in }{open R}^N,quad mathop {lim }limits_{|x|to infty } u(x) = 0.$$ A classical existence result by Berestycki and Lions [3] considers only the case when f is continuous. In this paper, we are interested in the existence of a solution when f is singular. For a singular nonlinearity f , Gazzola, Serrin and Tang [8] proved an existence result when $f in L^1_{loc}(mathbb {R}) cap mathrm {Lip}_{loc}(0,infty )$ with $int _0^u f(s),{rm d}s < 0$ for small $u>0.$ Since they use a shooting argument for their proof, they require the property that $f in mathrm {Lip}_{loc}(0,infty ).$ In this paper, using a purely variational method, we extend the previous existence results for $f in L^1_{loc}(mathbb {R}) cap C(0,infty )$ . We show that a solution obtained through minimization has the least energy among all radially symmetric weak solutions. Moreover, we describe a general condition under which a least energy solution has compact support." @default.
- W3000992283 created "2020-01-30" @default.
- W3000992283 creator A5006942801 @default.
- W3000992283 creator A5011646708 @default.
- W3000992283 creator A5023274338 @default.
- W3000992283 creator A5075367750 @default.
- W3000992283 date "2020-01-24" @default.
- W3000992283 modified "2023-10-16" @default.
- W3000992283 title "Least energy solution for a scalar field equation with a singular nonlinearity" @default.
- W3000992283 cites W1964635582 @default.
- W3000992283 cites W1973483534 @default.
- W3000992283 cites W1987033097 @default.
- W3000992283 cites W1997101540 @default.
- W3000992283 cites W2048645627 @default.
- W3000992283 cites W2060588871 @default.
- W3000992283 cites W2071132730 @default.
- W3000992283 cites W2073980661 @default.
- W3000992283 cites W2079387691 @default.
- W3000992283 cites W4240704356 @default.
- W3000992283 cites W46344860 @default.
- W3000992283 doi "https://doi.org/10.1017/prm.2020.4" @default.
- W3000992283 hasPublicationYear "2020" @default.
- W3000992283 type Work @default.
- W3000992283 sameAs 3000992283 @default.
- W3000992283 citedByCount "0" @default.
- W3000992283 crossrefType "journal-article" @default.
- W3000992283 hasAuthorship W3000992283A5006942801 @default.
- W3000992283 hasAuthorship W3000992283A5011646708 @default.
- W3000992283 hasAuthorship W3000992283A5023274338 @default.
- W3000992283 hasAuthorship W3000992283A5075367750 @default.
- W3000992283 hasConcept C105795698 @default.
- W3000992283 hasConcept C110521144 @default.
- W3000992283 hasConcept C114614502 @default.
- W3000992283 hasConcept C121332964 @default.
- W3000992283 hasConcept C134306372 @default.
- W3000992283 hasConcept C158622935 @default.
- W3000992283 hasConcept C186370098 @default.
- W3000992283 hasConcept C191640071 @default.
- W3000992283 hasConcept C202444582 @default.
- W3000992283 hasConcept C2524010 @default.
- W3000992283 hasConcept C33923547 @default.
- W3000992283 hasConcept C37914503 @default.
- W3000992283 hasConcept C57691317 @default.
- W3000992283 hasConcept C62520636 @default.
- W3000992283 hasConcept C9652623 @default.
- W3000992283 hasConceptScore W3000992283C105795698 @default.
- W3000992283 hasConceptScore W3000992283C110521144 @default.
- W3000992283 hasConceptScore W3000992283C114614502 @default.
- W3000992283 hasConceptScore W3000992283C121332964 @default.
- W3000992283 hasConceptScore W3000992283C134306372 @default.
- W3000992283 hasConceptScore W3000992283C158622935 @default.
- W3000992283 hasConceptScore W3000992283C186370098 @default.
- W3000992283 hasConceptScore W3000992283C191640071 @default.
- W3000992283 hasConceptScore W3000992283C202444582 @default.
- W3000992283 hasConceptScore W3000992283C2524010 @default.
- W3000992283 hasConceptScore W3000992283C33923547 @default.
- W3000992283 hasConceptScore W3000992283C37914503 @default.
- W3000992283 hasConceptScore W3000992283C57691317 @default.
- W3000992283 hasConceptScore W3000992283C62520636 @default.
- W3000992283 hasConceptScore W3000992283C9652623 @default.
- W3000992283 hasLocation W30009922831 @default.
- W3000992283 hasOpenAccess W3000992283 @default.
- W3000992283 hasPrimaryLocation W30009922831 @default.
- W3000992283 hasRelatedWork W12572453 @default.
- W3000992283 hasRelatedWork W22115408 @default.
- W3000992283 hasRelatedWork W25157485 @default.
- W3000992283 hasRelatedWork W25488507 @default.
- W3000992283 hasRelatedWork W26715833 @default.
- W3000992283 hasRelatedWork W28338598 @default.
- W3000992283 hasRelatedWork W6096220 @default.
- W3000992283 hasRelatedWork W7751177 @default.
- W3000992283 hasRelatedWork W8643771 @default.
- W3000992283 hasRelatedWork W9923627 @default.
- W3000992283 isParatext "false" @default.
- W3000992283 isRetracted "false" @default.
- W3000992283 magId "3000992283" @default.
- W3000992283 workType "article" @default.