6533b829fe1ef96bd128a350
RESEARCH PRODUCT
Compact embeddings and indefinite semilinear elliptic problems
Matthias Schneidersubject
Lemma (mathematics)Pure mathematicsLaplace transformFunction spaceApplied MathematicsWeak solutionMathematical analysisFunction (mathematics)Functional Analysis (math.FA)Mathematics - Functional AnalysisElliptic curveMathematics - Analysis of PDEsFOS: Mathematics35J65 35D05Lp spaceAnalysisAnalysis of PDEs (math.AP)Sign (mathematics)Mathematicsdescription
Our purpose is to find positive solutions $u \in D^{1,2}(\rz^N)$ of the semilinear elliptic problem $-\laplace u = h(x) u^{p-1}$ for $2<p$. The function $h$ may have an indefinite sign. Key ingredients are a $h$-dependent concentration-compactness Lemma and a characterization of compact embeddings of $D^{1,2}(\rz^N)$ into weighted Lebesgue spaces.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2002-06-07 |