Matches in SemOpenAlex for { <https://semopenalex.org/work/W4297748407> ?p ?o ?g. }
Showing items 1 to 69 of
69
with 100 items per page.
- W4297748407 abstract "In this note, we study Liouville theorems for the stable and finite Morse index weak solutions of the quasilinear elliptic equation $-Delta_p u= f(x) F(u) $ in $mathbb{R}^n$ where $pge 2$, $0le fin C(mathbb{R}^n)$ and $Fin C^1(mathbb{R})$. We refer to $f(x)$ as {it weight} and to $F(u)$ as {it nonlinearity}. The remarkable fact is that if the weight function is bounded from below by a strict positive constant that is $0<Cle f$ then it does not have much impact on the stable solutions, however, a nonnegative weight that is $0le f$ will push certain critical dimensions. This analytical observation has potential to be applied in various models to push certain well-known critical dimensions. For a general nonlinearity $Fin C^1(mathbb{R})$ and $f(x)=|x|^alpha$, we prove Liouville theorems in dimensions $nle frac{4(p+alpha)}{p-1}+p$, for bounded radial stable solutions. For specific nonlinearities $F(u)=e^u$, $u^q$ where $q>p-1$ and $-u^{q}$ where $q<0$, known as the Gelfand, the Lane-Emden and the negative exponent nonlinearities, respectively, we prove Liouville theorems for both radial finite Morse index (not necessarily bounded) and stable (not necessarily radial nor bounded) solutions." @default.
- W4297748407 created "2022-09-30" @default.
- W4297748407 creator A5065904836 @default.
- W4297748407 date "2011-09-23" @default.
- W4297748407 modified "2023-09-26" @default.
- W4297748407 title "Effect of weights on stable solutions of a quasilinear elliptic equation" @default.
- W4297748407 doi "https://doi.org/10.48550/arxiv.1109.5142" @default.
- W4297748407 hasPublicationYear "2011" @default.
- W4297748407 type Work @default.
- W4297748407 citedByCount "0" @default.
- W4297748407 crossrefType "posted-content" @default.
- W4297748407 hasAuthorship W4297748407A5065904836 @default.
- W4297748407 hasBestOaLocation W42977484071 @default.
- W4297748407 hasConcept C114614502 @default.
- W4297748407 hasConcept C119599485 @default.
- W4297748407 hasConcept C121332964 @default.
- W4297748407 hasConcept C127413603 @default.
- W4297748407 hasConcept C134306372 @default.
- W4297748407 hasConcept C138885662 @default.
- W4297748407 hasConcept C140031139 @default.
- W4297748407 hasConcept C14036430 @default.
- W4297748407 hasConcept C149288129 @default.
- W4297748407 hasConcept C158622935 @default.
- W4297748407 hasConcept C164154869 @default.
- W4297748407 hasConcept C179603306 @default.
- W4297748407 hasConcept C2780388253 @default.
- W4297748407 hasConcept C33923547 @default.
- W4297748407 hasConcept C34388435 @default.
- W4297748407 hasConcept C37914503 @default.
- W4297748407 hasConcept C41895202 @default.
- W4297748407 hasConcept C62520636 @default.
- W4297748407 hasConcept C78458016 @default.
- W4297748407 hasConcept C86803240 @default.
- W4297748407 hasConceptScore W4297748407C114614502 @default.
- W4297748407 hasConceptScore W4297748407C119599485 @default.
- W4297748407 hasConceptScore W4297748407C121332964 @default.
- W4297748407 hasConceptScore W4297748407C127413603 @default.
- W4297748407 hasConceptScore W4297748407C134306372 @default.
- W4297748407 hasConceptScore W4297748407C138885662 @default.
- W4297748407 hasConceptScore W4297748407C140031139 @default.
- W4297748407 hasConceptScore W4297748407C14036430 @default.
- W4297748407 hasConceptScore W4297748407C149288129 @default.
- W4297748407 hasConceptScore W4297748407C158622935 @default.
- W4297748407 hasConceptScore W4297748407C164154869 @default.
- W4297748407 hasConceptScore W4297748407C179603306 @default.
- W4297748407 hasConceptScore W4297748407C2780388253 @default.
- W4297748407 hasConceptScore W4297748407C33923547 @default.
- W4297748407 hasConceptScore W4297748407C34388435 @default.
- W4297748407 hasConceptScore W4297748407C37914503 @default.
- W4297748407 hasConceptScore W4297748407C41895202 @default.
- W4297748407 hasConceptScore W4297748407C62520636 @default.
- W4297748407 hasConceptScore W4297748407C78458016 @default.
- W4297748407 hasConceptScore W4297748407C86803240 @default.
- W4297748407 hasLocation W42977484071 @default.
- W4297748407 hasOpenAccess W4297748407 @default.
- W4297748407 hasPrimaryLocation W42977484071 @default.
- W4297748407 hasRelatedWork W2000603684 @default.
- W4297748407 hasRelatedWork W2005202046 @default.
- W4297748407 hasRelatedWork W2006715131 @default.
- W4297748407 hasRelatedWork W2012873039 @default.
- W4297748407 hasRelatedWork W2056947019 @default.
- W4297748407 hasRelatedWork W2078274926 @default.
- W4297748407 hasRelatedWork W2094628705 @default.
- W4297748407 hasRelatedWork W2354111432 @default.
- W4297748407 hasRelatedWork W2386891170 @default.
- W4297748407 hasRelatedWork W3189776940 @default.
- W4297748407 isParatext "false" @default.
- W4297748407 isRetracted "false" @default.
- W4297748407 workType "article" @default.