6533b830fe1ef96bd12967f9

RESEARCH PRODUCT

Robin problems with general potential and double resonance

Calogero VetroNikolaos S. PapageorgiouFrancesca Vetro

subject

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 growthMathematics

description

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.

yearjournalcountryeditionlanguage
2017-06-01Applied Mathematics Letters
https://doi.org/10.1016/j.aml.2017.01.003