Matches in SemOpenAlex for { <https://semopenalex.org/work/W4295109795> ?p ?o ?g. }
Showing items 1 to 59 of
59
with 100 items per page.
- W4295109795 abstract "We consider the semilinear elliptic problem begin{equation}label{problemAbstract} left{begin{array}{lr}-Delta u= |u|^{p-1}uqquad mbox{ in }B u=0qquadqquadqquadmbox{ on }partial B end{array}right.tag{$mathcal E_p$} end{equation} where $B$ is the unit ball of $mathbb R^2$ centered at the origin and $pin (1,+infty)$. We prove the existence of non-radial sign-changing solutions to eqref{problemAbstract} which are emph{quasi-radial}, namely solutions whose nodal line is the union of a finite number of disjoint simple closed curves, which are the boundary of nested domains contained in $B$. In particular the nodal line of these solutions doesn't touch $partial B$. The result is obtained with two different approaches: via nonradial bifurcation from the least energy sign-changing radial solution $u_p$ of eqref{problemAbstract} at certain values of $p$ and by investigating the qualitative properties, for $p$ large, of the least energy nodal solutions in spaces of functions invariant by the action of the dihedral group generated by the reflection with respect to the $x$-axis and the rotation about the origin of angle $frac{2pi}{k}$ for suitable integers $k$. We also prove that for certain integers $k$ the least energy nodal solutions in these spaces of symmetric functions are instead radial, showing in particular a breaking of symmetry phenomenon in dependence on the exponent $p$." @default.
- W4295109795 created "2022-09-10" @default.
- W4295109795 creator A5051584520 @default.
- W4295109795 creator A5068964305 @default.
- W4295109795 date "2017-09-11" @default.
- W4295109795 modified "2023-10-16" @default.
- W4295109795 title "Quasi-radial nodal solutions for the Lane-Emden problem in the ball" @default.
- W4295109795 doi "https://doi.org/10.48550/arxiv.1709.03315" @default.
- W4295109795 hasPublicationYear "2017" @default.
- W4295109795 type Work @default.
- W4295109795 citedByCount "0" @default.
- W4295109795 crossrefType "posted-content" @default.
- W4295109795 hasAuthorship W4295109795A5051584520 @default.
- W4295109795 hasAuthorship W4295109795A5068964305 @default.
- W4295109795 hasBestOaLocation W42951097951 @default.
- W4295109795 hasConcept C114614502 @default.
- W4295109795 hasConcept C121332964 @default.
- W4295109795 hasConcept C122041747 @default.
- W4295109795 hasConcept C134306372 @default.
- W4295109795 hasConcept C138885662 @default.
- W4295109795 hasConcept C2524010 @default.
- W4295109795 hasConcept C2780388253 @default.
- W4295109795 hasConcept C2781311116 @default.
- W4295109795 hasConcept C33923547 @default.
- W4295109795 hasConcept C41895202 @default.
- W4295109795 hasConcept C45340560 @default.
- W4295109795 hasConcept C62520636 @default.
- W4295109795 hasConcept C72409365 @default.
- W4295109795 hasConcept C96469262 @default.
- W4295109795 hasConceptScore W4295109795C114614502 @default.
- W4295109795 hasConceptScore W4295109795C121332964 @default.
- W4295109795 hasConceptScore W4295109795C122041747 @default.
- W4295109795 hasConceptScore W4295109795C134306372 @default.
- W4295109795 hasConceptScore W4295109795C138885662 @default.
- W4295109795 hasConceptScore W4295109795C2524010 @default.
- W4295109795 hasConceptScore W4295109795C2780388253 @default.
- W4295109795 hasConceptScore W4295109795C2781311116 @default.
- W4295109795 hasConceptScore W4295109795C33923547 @default.
- W4295109795 hasConceptScore W4295109795C41895202 @default.
- W4295109795 hasConceptScore W4295109795C45340560 @default.
- W4295109795 hasConceptScore W4295109795C62520636 @default.
- W4295109795 hasConceptScore W4295109795C72409365 @default.
- W4295109795 hasConceptScore W4295109795C96469262 @default.
- W4295109795 hasLocation W42951097951 @default.
- W4295109795 hasOpenAccess W4295109795 @default.
- W4295109795 hasPrimaryLocation W42951097951 @default.
- W4295109795 hasRelatedWork W1978042415 @default.
- W4295109795 hasRelatedWork W1980892922 @default.
- W4295109795 hasRelatedWork W2008992764 @default.
- W4295109795 hasRelatedWork W2017331178 @default.
- W4295109795 hasRelatedWork W2030128136 @default.
- W4295109795 hasRelatedWork W2075509416 @default.
- W4295109795 hasRelatedWork W2315492480 @default.
- W4295109795 hasRelatedWork W3037121695 @default.
- W4295109795 hasRelatedWork W3086542228 @default.
- W4295109795 hasRelatedWork W4200304685 @default.
- W4295109795 isParatext "false" @default.
- W4295109795 isRetracted "false" @default.
- W4295109795 workType "article" @default.