Search results for "35J65"

showing 2 items of 2 documents

Compact embeddings and indefinite semilinear elliptic problems

2002

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.

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)Mathematics
researchProduct

Local uniqueness of the solutions for a singularly perturbed nonlinear nonautonomous transmission problem

2020

Abstract We consider the Laplace equation in a domain of R n , n ≥ 3 , with a small inclusion of size ϵ . On the boundary of the inclusion we define a nonlinear nonautonomous transmission condition. For ϵ small enough one can prove that the problem has solutions. In this paper, we study the local uniqueness of such solutions.

Local uniqueness of the solutionsLaplace's equation020502 materialsApplied MathematicsNonlinear nonautonomous transmission problem010102 general mathematicsMathematical analysisA domainBoundary (topology)02 engineering and technology01 natural sciencesNonlinear systemMathematics - Analysis of PDEs35J25 31B10 35J65 35B25 35A020205 materials engineeringTransmission (telecommunications)Settore MAT/05 - Analisi MatematicaLocal uniqueness of the solutions; Nonlinear nonautonomous transmission problem; Singularly perturbed perforated domainFOS: MathematicsUniqueness0101 mathematicsSingularly perturbed perforated domainAnalysisMathematicsAnalysis of PDEs (math.AP)
researchProduct