6533b825fe1ef96bd1281f21

RESEARCH PRODUCT

Pairs of solutions for Robin problems with an indefinite and unbounded potential, resonant at zero and infinity

Francesca VetroCalogero VetroNikolaos S. Papageorgiou

subject

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

description

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.

yearjournalcountryeditionlanguage
2018-06-11
10.1007/s00229-018-1044-xhttp://hdl.handle.net/10447/345082