Compactness and existence results in weighted Sobolev spaces of radial functions. Part II: existence
| Autor: | Michela Guida, Sergio Rolando, Marino Badiale |
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| Přispěvatelé: | Badiale, M, Guida, M, Rolando, S |
| Jazyk: | angličtina |
| Rok vydání: | 2016 |
| Předmět: |
Sublinear function
Sobolev spaces of radial function 01 natural sciences Omega Combinatorics Nonlinear elliptic equation Mathematics - Analysis of PDEs FOS: Mathematics Compact embedding 0101 mathematics MAT/05 - ANALISI MATEMATICA Mathematics Applied Mathematics 010102 general mathematics Zero (complex analysis) Vanishing or unbounded potentials 010101 applied mathematics Sobolev space Elliptic curve Compact space Domain (ring theory) Vanishing or unbounded potential 35J60 (Primary) 35J20 35Q55 35J25 (Secondary) Analysis Energy (signal processing) Analysis of PDEs (math.AP) |
| Popis: | We prove existence and multiplicity results for finite energy solutions to the nonlinear elliptic equation \[ -\triangle u+V\left( \left| x\right| \right) u=g\left( \left| x\right| ,u\right) \quad \textrm{in }\Omega \subseteq \mathbb{R}^{N},\ N\geq 3, \] where $\Omega $ is a radial domain (bounded or unbounded) and $u$ satisfies $u=0$ on $\partial \Omega $ if $\Omega \neq \mathbb{R}^{N}$ and $u\rightarrow 0$ as $\left| x\right| \rightarrow \infty $ if $\Omega $ is unbounded. The potential $V$ may be vanishing or unbounded at zero or at infinity and the nonlinearity $g$ may be superlinear or sublinear. If $g$ is sublinear, the case with $g\left( \left| \cdot \right| ,0\right) \neq 0$ is also considered. Comment: 29 pages, 8 figures |
| Databáze: | OpenAIRE |
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