Search results for "indefinite and unbounded potential"

showing 2 items of 2 documents

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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Robin problems with general potential and double resonance

2017

Abstract We consider a semilinear elliptic problem with Robin boundary condition and an indefinite and unbounded potential. The reaction term is a Caratheodory function exhibiting linear growth near ± ∞ . We assume that double resonance occurs with respect to any positive spectral interval. Using variational tools and critical groups, we show that the problem has a nontrivial smooth solution.

Regularity theoryIndefinite and unbounded potentialApplied Mathematics010102 general mathematicsMathematical analysisInterval (mathematics)Function (mathematics)Robin boundary condition01 natural sciencesResonance (particle physics)Robin boundary conditionTerm (time)010101 applied mathematicsDouble resonance critical groupSettore MAT/05 - Analisi Matematica0101 mathematicsLinear growthMathematicsApplied Mathematics Letters
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