Bifurcation problems for superlinear elliptic indefinite equations
Keywords
Global bifurcation, uniform a priori bounds, moving plane, Kelvin transform, blow up analysisAbstract
In this paper, we are dealing with the following superlinear elliptic problem: $$\cases -\Delta u = \lambda u+h(x)u^p &\text{in }{\mathbb R}^N,\\ u\geq 0,\endcases\tag{P} $$ where $h$ is a $C^2$ function from ${\mathbb R}^N$ to ${\mathbb R}$ changing sign such that $\Omega^+ :=\{x\in {\mathbb R}^N\mid h(x)> 0\}$, $\Gamma :=\{x\in {\mathbb R}^N\mid h(x)=0 \}$ are bounded. For $1< p< {(n+2)}/{(n-2)}$ we prove the existence of global and connected branches of solutions of (P) in ${\mathbb R}^-\times H^1({\mathbb R}^N)$ and in ${\mathbb R}\times L^{\infty}({\mathbb R}^N)$. The proof is based upon a local approach.Downloads
Published
2000-09-01
How to Cite
1.
BIRINDELLI, Isabeau and GIACOMONI, Jacques. Bifurcation problems for superlinear elliptic indefinite equations. Topological Methods in Nonlinear Analysis. Online. 1 September 2000. Vol. 16, no. 1, pp. 17 - 36. [Accessed 23 September 2024].
Issue
Section
Articles
Stats
Number of views and downloads: 0
Number of citations: 0