6533b83afe1ef96bd12a6f77
RESEARCH PRODUCT
Multiple positive solutions for singularly perturbed elliptic problems in exterior domains
Riccardo MolleGiovanna Ceramisubject
Dirichlet problemPure mathematicsPartial differential equationApplied MathematicsMathematical analysisZero (complex analysis)Boundary (topology)Exterior domains; lack of compactness; multiplicity of solutionslack of compactnessDirichlet distributionExterior domainsmultiplicity of solutionssymbols.namesakeBounded functionDomain (ring theory)symbolsMathematical PhysicsAnalysisMathematicsdescription
Abstract The equation − e 2 Δ u + a e ( x ) u = u p −1 with boundary Dirichlet zero data is considered in an exterior domain Ω = R N ⧹ ω ( ω bounded and N ⩾2). Under the assumption that a e ⩾ a 0 >0 concentrates round a point of Ω as e →0, that p >2 and p N /( N −2) when N ⩾3, the existence of at least three positive distinct solutions is proved.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2003-09-01 |