Nodal solutions for a sublinear elliptic equation
✍ Scribed by Mikhaël Balabane; Jean Dolbeault; Hichem Ounaies
- Publisher
- Elsevier Science
- Year
- 2003
- Tongue
- English
- Weight
- 272 KB
- Volume
- 52
- Category
- Article
- ISSN
- 0362-546X
No coin nor oath required. For personal study only.
✦ Synopsis
We consider radial solutions of u + u -|u|
2 ) and prove by a shooting method the existence of compactly supported solutions with any given number of nodes.
📜 SIMILAR VOLUMES
We assert the locations of critical points constructed for the C 1 functional by the minimax method in terms of the order structures. These results are applied to nonlinear Dirichlet boundary value problems to obtain the multiplicity of nodal (sign-changing) solutions.
## Let be an arbitrary domain of R N and let be a nonnegative locally bounded Borel function on . In this paper, necessary and su cient conditions are obtained for the existence of a nonnegative nontrivial bounded solution to the sublinear elliptic equation u = (x)u in where 0 ¡ 6 1. The special c
The elliptic equation \(\Delta u+f(u)=0\) in \(R^{n}\) is discussed in the case where \(f(u)=\) \(|u|^{n} \quad u(|u| \geqslant 1),=|u|^{4} \quad{ }^{1} u(|u|<1), 10\). It is further proved that for any \(k \geqslant 0\) there exist at least three radially symmetric solutions which have exactly \(k\