Search results for "Lyapunov-Schmidt reduction method"

showing 2 items of 2 documents

Semilinear Robin problems driven by the Laplacian plus an indefinite potential

2019

We study a semilinear Robin problem driven by the Laplacian plus an indefinite potential. We consider the case where the reaction term f is a Carathéodory function exhibiting linear growth near ±∞. So, we establish the existence of at least two solutions, by using the Lyapunov-Schmidt reduction method together with variational tools.

Numerical AnalysisApplied Mathematics010102 general mathematicsFunction (mathematics)Mathematics::Spectral Theory01 natural sciencesTerm (time)010101 applied mathematicsComputational MathematicsSettore MAT/05 - Analisi MatematicaApplied mathematicsLyapunov-Schmidt reduction methodindefinite potential0101 mathematicsCarathéodory reactionLinear growthSemilinear Robin problemLaplace operatorAnalysisMathematicsComplex Variables and Elliptic Equations
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Pairs of solutions for Robin problems with an indefinite and unbounded potential, resonant at zero and infinity

2018

We consider a semilinear Robin problem driven by the Laplacian plus an indefinite and unbounded potential and a Caratheodory reaction term which is resonant both at zero and $$\pm \infty $$ . Using the Lyapunov–Schmidt reduction method and critical groups (Morse theory), we show that the problem has at least two nontrivial smooth solutions.

Pure mathematicsReduction (recursion theory)General Mathematicsmedia_common.quotation_subject010102 general mathematicsZero (complex analysis)Algebraic geometryRobin boundary conditionInfinity01 natural sciencesRobin boundary conditionNumber theoryresonance0103 physical sciencesLyapunov-Schmidt reduction method010307 mathematical physics0101 mathematicsindefinite and unbounded potentialcritical groupsLaplace operatorMathematicsMorse theorymedia_common
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