Topological Methods in Nonlinear Analysis

Bifurcation problems for superlinear elliptic indefinite equations

Isabeau Birindelli and Jacques Giacomoni

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Abstract

In this paper, we are dealing with the following superlinear elliptic problem: $$\begin{cases} -\Delta u = \lambda u+h(x)u^p &\text{in }{\mathbb R}^N,\\ u\geq 0,\end{cases}\tag{P} $$ 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.

Article information

Source
Topol. Methods Nonlinear Anal., Volume 16, Number 1 (2000), 17-36.

Dates
First available in Project Euclid: 22 August 2016

Permanent link to this document
https://projecteuclid.org/euclid.tmna/1471875420

Mathematical Reviews number (MathSciNet)
MR1805037

Zentralblatt MATH identifier
0970.35042

Citation

Birindelli, Isabeau; Giacomoni, Jacques. Bifurcation problems for superlinear elliptic indefinite equations. Topol. Methods Nonlinear Anal. 16 (2000), no. 1, 17--36. https://projecteuclid.org/euclid.tmna/1471875420


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